Persecution is defined as "unlawful coercion or punishment for religion's sake". (Lawful coercion or punishment is not considered persecution.) We see that scripture reveals clearly that those who follow Christ can expect to be persecuted:

"The servant is not greater than his master. If they have persecuted me, they will also persecute you..." (John 15:20)

"And all that will live godly in Christ Jesus, shall suffer persecution." (2 Tim. 3:12)

"And you shall be hated by all men for my name's sake: but he that shall persevere unto the end, he shall be saved. And when they shall persecute you in this city, flee into another." (Matt. 10:22-23)

Some people, mostly non-catholics, mistakenly use these quotes as a "sure proof" that the things they are personally doing and believing are true. Not so much a proof for others, but to make themselves feel satisfied with the path they have chosen to follow as if the "persecution" they perceive is some type of tangible sign of divine approval based on the fact that scriptures said it would happen!
Some Catholics also misunderstand the meaning of these words of scripture. There are some who likewise look to the persecution they receive as a sort of sign that their special stand on an issue, or apostolate, project, etc. is pleasing to God. This can often lead to an actual seeking after persecution itself somewhat akin to a martyr complex. Most often, in Catholics, this takes the form of making so much of "the fight" for the truth as to cause charity and prudence suffer. They forget the underlying principle in being "all things to all men", and feeding people with meat when they are only able to take milk (1 Cor. 3:2). In short, in their over-zealousness, they focus more on the truth they THEMSELVES are telling than on the circumstances and people they are speaking to, putting more pride in the fortitude they intend to practice than in the objective they are trying to reach - helping to convert a soul. The simplicity of the dove may be present here, but they forget the wisdom of the serpent, as Christ said, "Be ye, therefore, wise as serpents and simple as doves." (Matt. 10:16).
This fault is most often found in Catholics that are so weary of seeing the heresy and cowardice around them today, that they go to the other extreme and think, "I am going to FIGHT this error boldly, and I am NOT afraid if I get persecuted for it!" This attitude often tends to be reckless, and to satisfy "self", while being conducive to producing persecution. Since error is best fought by convincing (rather than turning a person away with the full and cold stark truth), we should heed the words of St. Paul:

"Let your speech be always in grace seasoned with salt: that you may know how you ought to answer every man." (Col. 4:6)

What is the correct understanding of the scriptural quotes concerning persecution? If we are persecuted, does this really mean that this is some divine proof that we have the truth and are doing the right thing? No. It merely means that those who follow Christ can EXPECT to be persecuted, but this is not a proof of anything in itself. Let us look at an analogy:

Given the true statement: "If it rains the grass therefore gets wet."

The reverse is NOT a logical conclusion: "If the grass is wet, it therefore rained."

We all know that when we see grass wet, it does not mean that it rained necessarily; it could be dew, or a sprinkler system. A follower of Christ, likewise, can expect persecution, but a person who is persecuted is not necessarily a follower of Christ. Persecution also suffered by Protestants and Jews on occasion but we cannot conclude that they are true followers of Christ, or that this is any kind of proof of righteousness. And for Catholics, bringing upon ourselves persecution foolishly, does not make us please God the more, as if persecution should be sought after as a good in itself. We must simply expect it.
Since persecution is itself unjust, we should still try to avoid it, and try to fight it. This is the practice of virtue; a struggle of trial and error that is not easy. If virtue were easy we would all be Saints. Moral virtue is the mean between two extremes - in this case, seeking to find the perfect balance in the varying situations of life between professing & promoting the faith without foolishly or unnecessarily bringing down upon us persecution. It is a virtue to fight and avoid persecution all the while uncomplainingly accepting, and using it to our merit, when we cannot avoid it.
Below is an article from the Catholic Encyclopedia (1913) that touches upon the virtue of the martyrs in respect to their persecution. While we always hear the stories of their torture and martyrdoms in such number, we don't often hear of the other side of their virtue in simultaneously taking prudent steps to avoid it.

Discipline of the Secret
(Latin "Disciplina Arcani".)

A theological term used to express the custom which prevailed in the earliest ages of the Church, by which the knowledge of the more intimate mysteries of the Christian religion was carefully kept from the heathen and even from those who were undergoing instruction in the Faith. The custom itself is beyond dispute, but the name for it is comparatively modern, and does not appear to have been used before the controversies of the seventeenth century, when special dissertations bearing the title "De disciplinâ arcani" were published both on the Protestant and the Catholic side.
The origin of the custom must be looked for in the recorded words of Christ: "Give not that which holy to dogs; neither cast your pearls before swine; lest perhaps they trample them under their feet, and turning upon you, they tear you" (Matt., vii, 6), while the practice in Apostolic times is sufficiently vouched for by St. Paul's assurance that he fed the Corinthians "as . . . little ones in Christ", giving them "milk to drink, not meat", because they were not yet able to bear it (I Cor., iii, 1-2). With this passage we may compare also Heb., v. 12-14, where the same illustration is used, and it is declared that "solid food is for the perfect; for them who by custom have their senses exercised to the discerning of good and evil." Although the origin of the custom is thus to be traced back to the very beginnings of Christianity, it does not appear to have been so general, or to have been carried out with so much strictness in the earlier centuries as it was immediately after the persecutions had ceased. This may be due in part to the absence of detailed information with regard to the earlier period, but it is probable enough that the discipline was growing more strict all through the second and third centuries on account of the pressure of persecution, and that, when persecution was at last relaxed, the need for reserve was felt at first, while the Church was still surrounded by hostile Paganism, to be increased rather than diminished. After the fifth or sixth century, when Christianity was thoroughly established and secure, the need of such a discipline was no longer felt, and it passed rapidly away. The practice of reserve (oikonomia) was exercised mainly in two directions, in dealing with catechumens, and with the heathen. It will be convenient to treat of these separately, as the reasons for the practice, and the mode in which it was carried out, differ somewhat in the two cases.

(1) Catechumens
It was desirable to bring learners slowly and by degrees to a full knowledge of the Faith. A convert from heathenism could not profitably assimilate the whole Catholic religion at once, but must be taught gradually. It would be necessary for him to learn first the great truth of the unity of God, and not until this had sunk deep into his heart could he safely be instructed concerning the Blessed Trinity. Otherwise tritheism would have been the inevitable result. So again, in times of persecution, it was necessary to be very careful about those who offered themselves for instruction, and who might be spies wishing to be instructed only that they might betray. The doctrines to which the reserve was more especially applied were those of the Holy Trinity and the Sacrament of the Holy Eucharist. The Lord's Prayer, too, was jealously guarded from the knowledge of all who were not fully instructed. With regard to the Holy Eucharist and the Lord's Prayer some relics of the practice still survive in the Church. The Mass of Catechumens, that earlier portion of the Eucharistic service to which learners and neophytes were admitted, and which consisted of prayers or readings from Holy Scripture and sometimes included a sermon, is still quite distinguishable, though the custom no longer survives in the Western Liturgy, as it does in the Eastern, of formally bidding the uninitiated to depart when the more solemn part of the service is about to begin. So also the custom of saying the Lord's Prayer in silence in all public services, except the latter part of the Mass, when catechumens would according to the ancient use no longer have been present, owes its origin to this discipline.
The earliest formal witness for the custom seems to be Tertullian (Apol. vii): Omnibus mysteriis silentii fides adhibetur. Again, speaking of heretics, he complains bitterly that their discipline is lax in this respect, and that evil results have followed: "Among them it is doubtful who is a catechumen and who a believer; all can come in alike; they hear side by side and pray together; even heathens, if any chance to come in. That which is holy they cast to the dogs, and their pearls, although they are not real ones, they fling to the swine" (Praescr. adv. Haer., xii). Other passages from the Fathers which may be cited are St. Basil (De Spir. Sanct., xxvii): "These things must not be told to the uninitiated"; St. Gregory Nazianzen (Oratio xi, in s. bapt.) where he speaks of a difference of knowledge between those who are without and those who are within, and St. Cyril of Jerusalem whose "Catechetical Discourses" are entirely built upon this principle, and who in his first discourse cautions his hearers not to tell what they have heard. "Should a catechumen ask what the teachers have said, tell nothing to a stranger; for we deliver to thee a mystery...see thou let out nothing, not that what is said is not worth telling, but because the ear that hears does not deserve to receive it. Thou thyself wast once a catechumen, and then I told thee not what was coming. When thou hast come to experience the hieght of what is taught thee, thou wilt know that the catechumens are not worthy to hear them" (Cat., Lect. i, 12). St. Augustine and St. Chrysostom in like manner stop short in their public addresses, and, after a more or less veiled reference to the mysteries, continue with: "The initiated will understand what I mean".
The Lord's Prayer was in St. Augustine's time taught eight days before baptism (Hom. xlii; cf. "Enchir.", lxxi, and the "Apostolic Constitutions", VII, xliv; St. Chrys. Hom. cc, al. xix, in Matt.). The Creed in like manner was taught just before baptism. So St. Ambrose, writing to his sister Marcellina (Epist xx, Benedict, ed.) says that on Sunday, after the catechumens had been dismissed, he was teaching the Creed in the baptistery of the basilica to those who were sufficiently advanced. (Cf. aslo St. Jerome, Epist. xxxciii, ad. Pammach.) More detailed teaching about the Holy Trinity and about the other sacraments was only given after baptism. Other passages which may be consulted are: Chrys., "Hom. in Matt.", xxiii, "Hom. xviii, in II Cor."; Pseud. Augustine, "Serm. ad Neoph.", i; St. Ambrose, "De his qui mysteriis initiantur"; Gaudentius, "Ser. ii ad Neoph."; Apost. Constit., III, v, and VIII, xi. The rule of reticence applied to all the sacraments, and no catechumen was ever allowed to be present at their celebration. St. Basil (De Spir. S. ad Amphilochium, xxvii) speaking of the sacraments says: "One must not circulate in writing the doctrine of mysteries which none but the initiated are allowed to see." For baptism reference may be made to Theodoret (Epitom. Decret., xcviii), St. Cyril of Alexandria (Contr. Julian., i), and St. Gregory Nazianzen (Orat. xl, de bapt.). The discipline with respect to the Holy Eucharist of course requires no proof. It is in involved in the very name of the Missa Catechumenorum, and one can scarcely turn to any passage of the Fathers which deals with the subject in which the reticence to be observed is not expressly stated. Confirmation was never spoken of openly. St. Basil, in the treatise already spoken of (De Spir. S., xxv, 11), says that no one has ever ventured to speak openly in writing of the holy oil of unction, and Innocent I, writing to the Bishop of Gubbio on the sacramental "form" of the ordinance answers: "I dare not speak the words, but I should seem rather to betray a trust than to respond to a request for information" (Epist. i, 3). Holy orders in the same way were never given publicly. The Council of Laodicea forbade it definitely in its speaking of the practice of begging the prayers of the faithful for those who are to be ordained, says that those who understand co-operate with and assent to what is done. "For it is not lawful to reveal everything to those who are yet uninitiated." So also St. Augustine (Tract xi. in Joann.): "If you say to a catechumen, Dost thou believe in Christ? he will answer, I do, and will sign himself with the Cross . . . Let us ask him, Dost thou eat the Flesh of the Son of Man and drink the Blook of the Son of Man? He will not know what we mean, for Jesus has not trusted himself to him."

(2) The Heathen
The evidence for the reserve of Christian writers when dealing with religious questions in books which might be accessible to the heathen is, naturally, to a large extent of a negative character, and therefore difficult to produce. Theodoret (Quaest. xv in Num.) lays down the general principle in terms which are quote clear and unmistakable: "We speak in obscure terms concerning the Divine Mysteries, on account of the uninitiated, but when they have withdrawn we teach the initiated plainly." That passage alone would suffice to refute the allegation not unfrequently made that the Discipline of the Secret was a confinement of the knowledge introduced in imitation of the heathen "mysteries". On the contrary all Christians were taught the whole truth, there was no esoteric doctrine, but they were brought to full knowledge slowly, and precautions were taken, as was very necessary, to prevent heathens from learning anything of which they might make an evil use. A very striking example of the way in which the discipline worked may be found in the writings of St. Chrysostom. He writes to Pope Innocent I to say that in the course of a disturbance at Constantinople an act of irreverence had been committed, and "the blood of Christ had been spilt upon the ground." In a letter to the pope there was no reason for not speaking plainly. But Palladius, his biographer, speaking of the same incident in a book for general reading, says only, "They overturned the symbols" (Chrys. ad Inn., i, 3 in P.G., LII, 534; cf. Döllinger, "Lehre der Eucharistie", 15). It is, no doubt, on this account that almost all the early apologists, as Minucius Felix Athenagoras, Arnobius, Tatian, and Theophilus, are absolutely silent on the Holy Eucharist. Justin Martyr and to a less degree Tertullian are more outspoken; the frankness of the former has been unduly urged to prove the non-existence of this institution in the first half of the second century. So again, as Cardinal Newman has observed (Development, 87), both Minucius Felix and Arnobius in controversy with heathens deny absolutely that Christians used altars in their churches. The obvious meaning was that they did not use altars in the heathen sense, and they must not be taken as denying the teaching of the Epistle to the Hebrews, that, in a Christian sense, "we have an altar".
The controversial importance of this subject in more recent times is, of course, obvious. The Catholics answered the accusation of Protestant writers, that their special doctrines could not be found in the writings of the early Fathers, by showing the existence of this practice of reserve. If it was forbidden to speak or write publicly of these doctrines, silence was completely accounted for. So again, if here and there in early writings terms were used which seemed to countenance Protestant teaching -- as for instance by speaking of the Holy Eucharist as symbols -- it became necessary always to examine whether these terms were not used intentionally to conceal the true doctrine from the uninitiated, and whether the same writers did not, under other circumstances, use much more definite language. Protestant controversialists, therefore, endeavoured first of all to deny that the practice had ever really existed, and then when they were driven from this position, they asserted that it was unknown to the earliest Christians, as shown by the freedom with which Justin Martyr speaks on the subject of the Holy Eucharist, and that it was the result of persecution. They alleged therefore that Catholics could not use it to account for the silence of any writer before the latter part of the second century at the earliest. To this Catholics responded that, although no doubt the practice may have been intensified through persecution, it goes back to the very beginnings of Christianity, and to Christ's own words. Moreover it can be shown to have been in force before St. Justin's time, and his action must be regarded as an exception, rendered necessary by the need for putting before the emperor an account of the Christian religion which should be true and full.
The monuments of the earliest centuries afford interesting examples of the principle of the Discipline of the Secret. Monuments which could be seen by all could only speak of the mysteries of religion under veiled symbols. So in the catacombs there is scarcely any instance of a painting the subject of which is directly Christian, although all spoke of Christian truth to those who were instructed in their meaning. Jewish subjects typical of Christian truths were commonly chosen, while the representation of Christ under the name and form of a fish (see FISH) made the allusion to the doctrine of the Holy Eucharist possible and plain. There is, for example, the famous Autun inscription (see PECTORIUS): "Take the food, honey-sweet, of the redeemer of the saints, eat and drink holding the Fish in they hands"; words which every Christian would understand at once, but which conveyed nothing to the uninitiated. The inscription of Abercius (q.v.) offers another notable instance.
The need for this reticence became less pressing after the fifth century, as Europe became Christianized and the discipline gradually passed away. We may, however, still trace its effects in the seventh century in the absurd understatements contained in the Koran on the subject of the Blessed Trinity and the Holy Eucharist. This, perhaps, is almost the last instance which could be brought forward. Once the doctrines of the Church had been publicly set forth, any such discipline became impossible and no return to it was practicable. For a refutation of the theory of G. Anrich (Das Antike Mysterienwesen, 1894), that the primitive Christians borrowed this practice from the mysteries of Mithra, see Cumont, "The Mysteries of Mithra" (London, 1903), 196-99.