The situation is this. I maintain that, to hold to the notion that the accounts are historical, one has to jump through hoops. However, the Christian might say that one or two claims in the accounts may be false, but that does not mean that the other claims are false. But in this approach lie many issues. For example:
1) If we accept that some claims in the accounts are false, does the Christian special plead that the other claims are true?
2) The claims are so interconnected that to falsify one or two of them means that the house of cards comes tumbling down.
3) If we establish that at least some of the claims are false, how does this affect other claims within the same Gospel? How can we know that claims of Jesus' miracles are true given that the reliability of the writer is accepted as questionable?
And so on. In my book, The Nativity: A Critical Examination, I think I give ample evidence that allows one to conclude that the historicity of the nativity accounts is sorely and surely challenged. All of the aspects and claims, that is. There are problems, for sure, if one accepts that some claims are false but others are true. But the simple fact of the matter is that all of the claims are highly questionable.