Using the enemy's sword?

I have been reading about inter-religion debates. In this particular instances, claims that the Bible contains references to Muhammad and claims that the Koran confirms the divinity of Jesus. Obviously, some Muslims use the former and some Christians use the latter to attack each other.

I find it contradictory that people use other people's scripture as a basis for their argument. When people say that certain passages in the Bible predict the coming of Muhammad, are they saying that they believe in the Bible? The Bible contains much more passages about the beliefs of Judaism and Christianity. Do they also believe in those passages? I know that some Muslims believe that the Bible has been corrupted. In this light, are they saying that only those pro-Islam passages are still un-corrupted?

Likewise, what are Christians who use the Koran argument implying? Do they selectively believe certain passages of the Koran while ignoring the passages that reject Jesus' divinity? I think the real argument they are presenting is that the Koran has contradictions, rather than for Muslims to believe that Jesus is God.

What's the point? Exactly.