I do not mean to be rude, but your reply is riddled with egregious fallacies and clumsy cognitive errors. Such errors, as will be demonstrated, are common amongst those who serve their own egocentric beliefs over the truth.
It is not the truth you seek, but the mere reaffirmation of your pre-established beliefs in Christ. You are not concerned with reason or truth; you are concerned with marshaling rationalizations in order to confirm your outdated and illogical supernatural beliefs.
Before I begin highlighting the seemingly shrewd errors in your poor reply, I should point to a mistake I made, so that I do not cast stones without first reflecting upon my own shortcomings, as is the message in that Platonic and forged/interpolated story in “John” (The Woman Taken in Adultery – “John” 8:1-11).
I mistakenly said; “Take for example, the empty yet manipulative and provocative promises made within the following words of one of the most renowned apostolic fathers, Polycarp…” What I should have said was, “within the following words contained in a letter written by an apostolic father pertaining to one of the most renowned martyrs, Polycarp;” however, such a minor error does not detract from the substance of my argument, an argument that, regardless of your twisting and contorting of facts, your reply does not adequately address.
I contend that there was a culture of aggressive voluntary martyrdom within the early Church, for if there wasn’t, it is rather baffling as to why many early Church fathers, as you rightly pointed out, would rail against such a “non-existent” practice. Having said this, your faith-induced myopia appears to have caused you to see a handful of written sources as representing a “consensus,” which you appear to imply, displays the actual historical circumstances regarding aggressive and voluntary martyrdom, rather than taking into account the broader social psychological, and historical context of the culture of aggressive voluntary martyrdom in the early Church.
The sources I employed to make my point were used correctly and do demonstrate that;
1. Aggressive and Voluntary Martyrdom was an issue in the early Church
In further support of this historical fact, please read Geoffrey de Ste. Croix, Michael Whitby, and Joseph Streeter’s Christian Persecution, Martyrdom and Orthodoxy, in which Croix demonstrates the prevalence of aggressive and voluntary martyrdom in the early Church, as well as clearly showing how such provocation contributed to the wider implementation of persecution by antagonizing Roman governors, most of whom were predisposed to be tolerant.
2. This proactive suicide did provide a symbolically significant and successful marketing tool for a religion that is built on the myth/legend of a resurrected Jewish/pagan-styled martyr.
To this point, William Goodwin Aurelio Professor of the Appreciation of Scripture at Boston University, Paula Fredrickson says:
“The martyrs are a heroic minority. They don’t represent a huge popular swelling. We don’t have tens of thousands of people being martyred. What we do have, is tens of thousands of people admiring the few who are martyred.”
Further to this point, W.H.C. Frend, in his book, Martyrdom and Persecution in the Early Church: A Study of a Conflict from the MacCabees to Donatus, says:
“Persecution was seen by early Christians, as by later historians, as one of the crucial influences on the growth and development of the early Church and Christian beliefs.” 
Further still, I might cite the Cambridge History of Christianity, from which we learn:
The demographic study of earliest Christianity began with Adolf von Harnack’s Die Mission und Ausbreitung des Christentums. Relying on the critical analysis of literary sources, Harnack saw demographically significant Christian communities wherever there was a martyrdom narrative…
And I could continue to cite sources to bolster this historical fact ad infinitum.
Regarding my use of the Martyrdom of Polycarp, you said:
“Just 115 words later in chapter four it recounts that a Phrygian man named Quintus who sought voluntarily martyrdom, but when he saw the fate awaiting him he apostatized instead. The letter then admonishes the Christians, “Wherefore, brethren, we do not commend those who give themselves up [to suffering], seeing the Gospel does not teach so to do.”
This is classic data-mining on your part, which is a common tactic employed by religious apologists, who, when confronted with a mass of data, select that which is beneficial to the aims of his or her cult/religion.
Why did the author of the Martyrdom of Polycarp condemn Quintus? What is the purpose of the Martyrdom of Polycarp? Is it not to establish and promote an ideology of martyrdom, one that distinguishes between the correct and incorrect means by which one is to kill one’s self for Jeebus? What, according to the Martyrdom of Polycarp, is the right way to kill one’s self? These are the questions your little data-mining expedition sailed, either cunningly or clumsily, around. One must have received visions/hallucinations, or at least said they did, before they could go down in history as a glorified Christian Jihadi and such was the case with Polycarp, who, if we are to believe such fanciful and superstitious stories, had a vision of his pillow on fire and then, like the disturbed patient of an insane asylum, jumped up and exhorted, “I must be burnt alive!”
I do concede that Church Fathers spoke out against voluntary martyrdom and I made that very point, but if, as you suggest, aggressive and voluntary martyrdom was not a factor in the early Church, why then were these Church Fathers speaking out against an allegedly non-existent phenomenon? Just in case? I have yet to see a road sign that says “Don’t strap your infant to the roof of your car!” I have seen signs that say “don’t drink and drive,” because that phenomenon actually exists and is prevalent enough to warn against.
To provide you with yet another example of how you data-mine, I would like to draw your attention to the fact that you quoted Tertullian in your first reply, yet, having allegedly read Tertullian, and at the same time, denying the existence of aggressive voluntary martyrdom, you failed to cite Tertullian’s praising of a number of Carthaginian Christians who voluntarily approached a Roman governor (Antoninus), wishing to be executed for their faith. Nor did you even acknowledged the fact that Tertullian supported the notion of voluntary martyrdom, or that such outspoken support of that insane practice did bestow upon the deluded volunteer, social status as well as, according to the apostolic father who authored the Martyrdom of Polycarp, a seat up in space with a legendary son of a mythical god.  Finally, you failed to consider the impact that such literature proved to have over the minds of deluded martyrs that followed in Polycarp’s gullible footsteps.
In my reply, I did not mean to imply that the intentions of Church leaders were altogether deliberately sinister or misleading, leaders whose works inspired such an insane and ultimately fruitless waste of human life, for I am almost certain that they were, as you are today, convinced of their shared and superstitious delusions. The ambitions I spoke of pertained to the growth of the Church, which, like any human endeavor, would have had both sincere and pure intentions behind it, as well as more greedy and political ones. After all, Christianity is of human contrivance. I was merely highlighting the existence of the culture of aggressive and voluntary martyrdom, as well as enunciating the fact that such a culture was a factor which helped increase the numbers of early Christians; and that such a practice is violent in nature. The ante-Nicene period is not the primary focus of the meme I created and I wait with baited breath for you to defend the inexcusable violence of your profane religion from the 4th century to the 19th,.
Now, your second reply titled: ‘Don’t Blame Christian Martyrs for Violence’  is even sloppier and more rhetoric-ridden than the one I have just addressed. I don’t blame the martyrs, although I do think that they died for nothing, for killing or dying for one’s superstitions is a very stupid thing to do, however, my argument was based on the following facts:
1. Church fathers wrote works that engendered and encouraged an ideology of martyrdom.
2. Numbers of Christians were influenced by said ideology and offered themselves up as voluntary martyrs.
3. Public martyrdoms were a factor in the rise and growth of the early Church.
4. Inciting martyrdom is an incitement to violence against the gullible, yet innocent martyr.
Once again, the emphasis of my meme deals with Christianity in the Post Nicene period (4th – 19th centuries), as this is when Christianity became a major religion. Had it not been for Constantine, Christianity would probably not be a major religion today. Now, let me put that another way. Had it not be for the help of a pathological and psychopathic Roman emperor, an emperor who boiled his wife alive and executed his own son, Christianity would probably not be a major religion today..
In this anti-intellectual and rhetoric-laced reply, you wrote:
Even today, Christians are the most persecuted people in the world because of their faith. Reports out of Nairobi and other nations about gunmen hunting down Christians in shopping malls are horrifying. Does Sherlock label this “Christian violence?” Does he think that the dozens who died simply because they were attending All Saints’ Church staged it for the PR value? Such claims would rightfully be considered disgusting and offensive. Just because the early martyrs preceded these by some 1700 years doesn’t make Sherlock’s claims any less so.
Having made my position clear (I don’t blame the martyrs), I would like to say that I find it disturbing, yet wholly unsurprising, that you would stoop to such pathos-provoking theatrics. These questions and statements are rather ironic, particularly given that I am the founder and co-chair of an organization (Human Rights for Atheists Agnostics and Secularists) that is seeking to alleviate the suffering of human beings (including Christians) occasioned by religious persecution worldwide.
On a final note, Christians are not the most persecuted people in the world. Women and homosexuals are far more persecuted (per-capita), and largely as a result of religions like yours, religions that for no valid reason have oppressed, persecuted and infringed upon their human rights, merely so they might protect and propagate a shared delusion.
As much as I would love to continue pointing out your cognitive errors and logical fallacies, I am very busy, but you may rest in the notion that no matter what I say, no matter how much evidence I present, your faith in your highly improbable god will not be destroyed, and for no other reason than the fact that your faith is, at least for the moment, impervious to reality.
1. Geoffrey de Ste. Croix, Michael Whitby, and Joseph Streeter. Christian Persecution, Martyrdom and Orthodoxy. Oxford University Press (2006).
3. W.H.C. Frend. Martyrdom and Persecution in the Early Church: A Study of a Conflict from the MacCabees to Donatus. Baker Pub. Group (1981).
4. Frank Trombley. Overview: the geographical spread of Christianity, cited in; Margaret M. Mitchell & Frances M. Young. Cambridge History of Christianity, Vol. 1. Cambridge University Press. (2008). p. 302.
5. Come Reason’s Apologetics Notes: ‘Were early Christians encouraged to become martyrs?’ http://apologetics-notes.comereason.org/2014/07/were-early-christians-encouraged-to.html#.U78wglLlqig
6. Philip Schaff. Ante-Nicene Fathers Volume 1; The Martyrdom of Polycarp, Grand Rapids, MI: Christian Classics Ethereal Library. p. 113.
7. The Address of Q. Sept. Tertullian, To Scapula Tertullus, Proconsul of Africa. Tr. by Sir David Dalrymple (1790):
(Take heed, SCAPULA, lest we, who undergo such unutterable hardships, should all of us at once break forth and shew, that so far from dreading, we spontaneously call for tortures. While Arrius Antoninus was zealously persecuting the Christians in Asia, they came uncalled, and in one body, before him. Having doomed some few of them to death, he said uto the rest, “Wretches, if ye must needs die, have you not crags and halters!” Should the Christians here act like those of Asia, what wouldst thou do to so many thousands, men and women, young and old, and of every station, yielding themselves up uncalled at thy tribunal…For every one beholding such wonderful endurance, becomes perplexed in his mind, and then is led eagerly to inquire what Christianity is; and on his finding out, he follows THE TRUTH.)
8. William Tabbernee. Fake Prophecy and Polluted Sacraments. Brill. (2007) p. 419.
9. Philip Schaff. Ante-Nicene Fathers. Vol. 1: The Apostolic Fathers with Justin Martyr and Irenaeus. The Martyrdom of Polycarp. Christian Ethereal Library. (1885).p. 66.
10. Come Reason’s Apologetic Notes; ‘Don’t Blame Christian Martyrs for Violence;’ http://apologetics-notes.comereason.org/2014/07/dont-blame-christian-martyrs-for.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+ComeReasonsApologeticsNotes+(Come+Reason’s+Apologetics+Notes)#.U784IlLlqig