In part 1 of this series, I explained that Matthew's and Luke's stories of Jesus' birth don't just contain different information, but are actually contradictory in several important ways. It's worth pointing out that the fact that they contradict each other doesn't mean that, at least in theory, one of them could be historical and other not be. For example, maybe Matthew's telling us the real story and Luke's making it up. Or vice versa.
Although this possibility should be considered, more detailed examination of both narratives shows that each has major features that are very likely not historical. Events from Matthew and Luke will be the subject of future installments of this series.
But now, on two reason #2 after the jump.
2. Outside of Matthew and Luke, our earliest New Testament writings show no awareness of Jesus' birth having any extraordinary circumstances, suggesting that accounts of his birth are a relatively late accretion to the gospel traditions about Jesus' life. The Gospel of Mark, widely considered to be the earliest of the four canonical gospels (written around the year 70, 40 years after Jesus' death), has nothing to say about Jesus' birth. Moreover, Mark begins his gospel with the words, "The beginning of the good news (or Gospel) of Jesus Christ"--and then proceeds to narrate Jesus' baptism. Some early Christians took this to mean that Jesus only became God's Son at the moment of his baptism, when the Holy Spirit descended upon him and a divine voice from the heavens said, "You are my Son, the Beloved." (Mark 1:10-11)
So Mark does not appear to have known any traditions about Jesus' birth. Matthew and Luke are generally thought by scholars to have used Mark as one of their sources, and each of them seems to have dealt with the lack of a birth story in their own way. And the Apostle Paul, whose letters are the earliest Christian writings (written in the 50s), only says in Galatians 4:4 that Jesus was "born of a woman, born under the Law." All this means is that Jesus had a mother and he was born a Jew. So nothing very specific about the events surrounding Jesus' birth there.
The Gospel of John does not contain any information about Jesus' birth either. John may well be the latest of the four canonical gospels, believed by many scholars to have been written around 90--though the reasons that are put forward for this are, in my opinion, not very good. But whether John was the latest canonical gospel, the earliest canonical gospel, or somewhere in between, the fact remains that John has nothing to say about Jesus' birth.
Furthermore, there is an intriguing passage wherein John could have said something about Jesus' birth, but didn't. In John 7:40-43, a crowd is debating Jesus' Messianic credentials. Some were saying he was the Messiah, but others were saying, "No way! The Messiah's from Bethlehem, not Galilee!" (my paraphrase) John might have chosen this occasion to argue in favor of Jesus' birth in Bethlehem, had he known a tradition that Jesus was born there. But he says nothing. So maybe he'd never heard a story about Jesus being born in Bethlehem. Or maybe he had, but considered it dubious. In any case, he does not defend a birth in Bethlehem.
So, when we look at the other gospels and the writings of the Apostle Paul (not to mention all the other NT writings, none of which say anything about Jesus' birth in Bethlehem), we find that the "Christmas story" is in fact restricted only to Matthew and Luke. Compare this with, for example, the information that Jesus died on a cross, which is found in all four gospels (as well as in several pre-gospel sources), Paul's letters, and nearly every other NT writing. If we think of the development of traditions about Jesus' life and teachings as a snowball, accumulating more and more material as it goes along, then the infancy narratives are a very late layer. In contrast, the first Christians cared much more about the end of Jesus' life (the passion narratives) and his teachings (the sayings tradition) than about his birth--those are the traditions about Jesus that are extremely widespread, not his birth.