The Stoics and Cynics, you might recall, seem to have taken the Christians to be zealots eager to die because they had excited their imaginations with fantastic stories. It's perhaps unsurprising, then, that Justin responds by emphasizing the ways in which both Stoic philosophers and their philosophical heroes insisted on dying when the matter was forced upon them:
And those of the Stoic school--since, so far as their moral teaching went, they were admirable, as were also the poets in some particulars, on account of the seed of reason [the Logos] implanted in every race of men-- were, we know, hated and put to death,--Heraclitus for instance, and, among those of our own time, Musonius and others. For, as we intimated, the devils have always effected, that all those who anyhow live a reasonable and earnest life and shun vice, be hated.
Contrary to the Cynic accusation, he argues, Christians do not rush toward their deaths; but death is a debt every human being must pay, and Christians, understanding the true nature of the world, give thanks when they pay that debt. This fearlessness in the face of death shows forth the true value of virtue, and, Justin notes, led to his own conversion:
For I myself, too, when I was delighting in the doctrines of Plato, and heard the Christians slandered, and saw them fearless of death, and of all other things which are counted fearful, perceived that it was impossible that they could be living in wickedness and pleasure. For what sensual or intemperate man, or who that counts it good to feast on human flesh, could welcome death that he might be deprived of his enjoyments, and would not rather continue always the present life, and attempt to escape the observation of the rulers; and much less would he denounce himself when the consequence would be death?...For I myself, when I discovered the wicked disguise which the evil spirits had thrown around the divine doctrines of the Christians, to turn aside others from joining them, laughed both at those who framed these falsehoods, and at the disguise itself, and at popular opinion; and I confess that I both boast and with all my strength strive to be found a Christian; not because the teachings of Plato are different from those of Christ, but because they are not in all respects similar, as neither are those of the others, Stoics, and poets, and historians.
Who does not have the faith of the martyrs, does not have the faith.