One of my teachers used to be Christian but converted to Judaism for a fiancée with whom he eventually broke up. Recently he approached me and said that he was looking to convert back to Christianity, but he seriously disagrees with "the divinity of the birth of Christ." How should I respond?
It is a little difficult to assess what he means, because he isn’t using standard language. He may mean that he disagrees with the fact that Christ is God, disagrees with the fact that Christ was born of a virgin, or both.
A first step would be to ask what he means—which of these three he has in mind (or whether he has a fourth in mind).
If he disagrees with the fact that Christ is God, one could point him to passages in the New Testament, like John 8:58, that indicate that Christ is God. Once he sees that the New Testament teaches that Christ is God he can then go on to read books supporting the reliability of the New Testament; in particular, books showing the truth of the Resurrection of Christ. If Christ rose from the dead then he is qualified to tell us who he is, and if he tells us he’s God, we should believe him.
If he has trouble believing in the Virgin Birth of Christ, one could point out that God created the entire universe, and so if he wants to he can create the single cell needed to cause a virgin to conceive. God is infinitely powerful, so coming up with a single cell to cause a virgin to conceive is infinitely easy for him, just like creating the universe was.
Once a conceptual difficulty like this is cleared away, it is a simple matter to show that the New Testament teaches that Christ was born of a virgin, and again we’re back to the subject of the reliability of the New Testament.
He may also have other conceptual difficulties that need to be cleared away, either pertaining to the divinity of Christ or the Virgin Birth, but these difficulties can only be surfaced and dealt with by talking to him. In particular, ask what difficulties he feels with the doctrine.
One also could consider giving him a copy of Mere Christianity and possibly Miracles by C. S. Lewis. Even though these are not (entirely) focused on the topics he may be having a problem with, they can provide a useful role in helping reintroduce him to the Christian mindset and the fact that God can work whatever miracles he wants.