One of the hardest things about apologetics is that while people are often blind to their own biases, they are certainly not biased towards yours. If you're a Christian, anything you say is automatically assumed to be a biased statement, reducing its truth value in their eyes. Citing Christian sources in defence of Christianity is seen as a bad thing, whereas it is somehow more effective if you can find a non-Christian saying something nice about Christianity. This ultimately means the same statement has different value coming from different mouths.
This is a tragically illogical state of affairs. First, bias is not a thing limited to Christians. No being capable of independent thought is immune to bias. Not being Christian doesn't make you unbiased, it makes you biased towards whatever view you hold in its stead. Are you an atheist? You're biased towards atheism. Are you a Muslim? You're biased towards Islam. Are you a Buddhist? You're biased towards Buddhism. Whatever you believe, you are biased towards that belief.
And that's actually not a bad thing in and of itself. To be sure, it can be a bad thing. If you are blind to your bias, it will prevent you from thinking clearly about other views. Furthermore, if you are so biased that if your view is wrong, you don't want to be right, that's a major problem. But if you recognise, and are willing to lay aside your biases, you are a rational thinker.
By contrast, picture someone so unbelievably biased, he will say "yes, all the evidence points to Christianity, but I still refuse to believe it". Even if you are not a Christian, you should be able to see the problem with this. It's as bad as saying "all the evidence points away from Christianity, but I still believe it". Following your biases isn't irrational, it's honest.
To illustrate this, consider these two pieces of first century historians talking about Jesus. First, let's look at Josephus. Josephus was a first century Jewish historian who famously wrote Antiquities of the Jews. Though by no means a Christian himself, Josephus is often cited as an extra-biblical example of early evidence for Christ. This is not the context in which I am mentioning him, however. One of his more controversial statements is "About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who performed surprising deeds and was a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Christ. And when, upon the accusation of the principal men among us, Pilate had condemned him to a cross, those who had first come to love him did not cease. He appeared to them spending a third day restored to life, for the prophets of God had foretold these things and a thousand other marvels about him. And the tribe of the Christians, so called after him, has still to this day not disappeared."
This statement, for obvious reasons, is of disputed authenticity. Why? Because the statement doesn't agree with the bias of the supposed author. If Josephus believed Jesus was the Christ, why did he not become a Christian? Therefore, historians doubt the passage's authenticity, believing the general framework belonged to Josephus, but that a Christian edited it at some later point.
Compare this with 2 Peter 1:16-21: "For we have not followed cunningly devised fables, when we made known unto you the power and coming of our Lord Jesus Christ, but were eyewitnesses of his majesty. For he received from God the Father honour and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased. And this voice which came from heaven we heard, when we were with him in the holy mount. We have also a more sure word of prophecy; whereunto ye do well that ye take heed, as unto a light that shineth in a dark place, until the day dawn, and the day star arise in your hearts: Knowing this first, that no prophecy of the scripture is of any private interpretation. For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost."
This statement agrees with Peter's bias, because Peter's bias leads him to that statement. If he made that statement but didn't believe it, he's a liar. By the same token, if he believed it, but didn't say it, he's a liar. Because Peter's bias matches his statement, he can be taken as honest.
You see, then, that bias is not a problem when it is recognised, and in fact is a very admirable character trait. But what's more interesting is that biased statements from the right sources can be weightier than others. See, Peter, unlike Josephus, is in a position to verify his bias. He isn't hearing two opposing cases and deciding which one sounds stronger. Nor is he gathering evidence and drawing a conclusion that could be easily changed if more evidence is found. Rather, Peter is a direct witness. He is a biased, yet also primary source. Thus, his testimony alone can be taken with, but also apart from other, extra-biblical evidence, be it hostile sources like Josephus or the Talmud, or other Christian sources.
And so we see that bias is not a reason to reject, ignore, or even give less weight to a source. Rather, evidence presented by such a source should be judged on its own merits. The evidence for Christianity may come primarily from Christian sources, but that's only because if the evidence points to Christianity, only a liar would not become a Christian. One might just as easily say the evidence against Christianity comes primarily from anti-Christian sources. Is it rational to do this? Certainly not. I would have no role as an apologist if all I had to do to deal with anti-Christian arguments was say "of course you'd say that, you're biased". The correct attitude is to acknowledge the fact that we are all biased, and we all need to recognise it, lest we become the kind of fools described in Proverbs 18:2.