Mark Goodacre has argued on his recent podcast that Jesus was likely born and raised in Nazareth (listen here). It is his contention that it makes more historical sense. The authors of the Gospel of Matthew and the Gospel of Luke read in the prophet Micah (5:2) that the Messiah would come from Bethlehem. This was the motivation for creating the birth narratives about Jesus being born in Bethlehem.
N.T. Wright is quoted in the podcast as arguing that we have two independent traditions in Matthew and Luke and therefore we have no reason to think that the tradition is not historical. This is dependent on the theory that Matthew and Luke are dependent on Mark. If Mark is not the earliest gospel, but rather Matthew it is possible that we do not have two independent traditions for Jesus being born in Bethlehem, but rather one (Luke being dependent on Matthew).
In addition, Goodacre notes that in the Gospel of John the author is concerned with Jesus coming from heaven. Therefore, he does not really care if Jesus came from Bethlehem or Nazareth. This is why the author can note that some did not believe that Jesus was the Messiah without being defensive. The author writes that some were troubled because Jesus came from Galilee when these people believed the Messiah had to come from Bethlehem (see John 7:42).
The Bethlehem tradition would have been a major hurdle for some Jews. If Jesus was born elsewhere he could not be Messiah. For these people Matthew and Luke present a story that has Jesus being born in Bethlehem before being moved to Nazareth later.
Doug Chaplin responds with reasons for why he thinks Jesus was born in Bethlehem (read here). He does not think that Luke is dependent on Matthew, so this would revive the two independent traditions argument. Also, he points out that there was no clear “Bethlehem tradition” in Second Temple Judaism messianic expectations. Finally, he provided some further points regarding The Infancy Gospel of James as well as the Pauline tradition (see Romans 1:3-4).
I’d encourage anyone interested to listen to Mark’s podcast as well as read Doug’s response. Each give good arguments for believing that Jesus was born in Nazareth and Bethlehem, respectively.
Update: NT Wrong chimes in here.