I have been studying this subject for some time now and it looks like I will be for some time yet, but I will try to answer this question as precisely as possible without writing a twelve-page essay on it. =)
First of all, it's not self-defense that's the problem, it's using force (or, more usually, deadly force) that's the problem. Those who say they are against using force have no problem with and in fact advocate other means (usually, prayer or occasionally singing).
They typically back this up by arguing that the New Testament teaches a kind of pacifism not found in the Old Testament. While I applaud their good intentions in trying to reduce the amount of violence in the world, and though I must admit I find their system attractive, I simply cannot find it in the Bible. The New Testament passages they cite most commonly, in Matthew 5, either refer to interpersonal insults (not bodily harm or death) or religious persecution. Those two passages form the crux of their argument, and without those the rest of their New Testament case has little to no direct application to self-defense.
That said, let's take a look at the Old Testament. In the Old Testament, self-defense was permitted, but with restrictions. For example, it was lawful to kill a thief, if he broke into one's house at night; but if a thief was caught breaking in in daylight and was killed, the one who killed him was guilty of murder.
Furthermore, David sets an example when he flees from King Saul rather than standing up in self-defense. I tend to suspect that this implies that we ought not to act in self-defense against lawful governmental authorities, but I wouldn't stake anything on that until I've studied it further. Nonetheless, he certainly does not shy away from self-defense in other cases.
There may be other examples as well. I've barely scratched the surface thus far in my study, but I hope to eventually compile a more or less comprehensive exegesis of the pertinent texts--maybe ten or twenty years down the road, I don't know.
Did that help at all? I can elaborate on some points (not all of them, but the New Testament ones at least) if you like.
