Excerpt from: “Why I am not a Christian” by Keith M. Parsons
Matthew and Luke make the same three major claims about Jesus’ birth: that it was a virgin birth, that it took place in Bethlehem, and that Jesus was of Davidic descent. But the evidence to back up these claims is quite different in the two accounts. In Luke, the annunciation of the birth is made to Mary; in Matthew it is made to Joseph. Matthew has Joseph and Mary marry; Luke does not. Both offer genealogies to prove Jesus’s Davidic lineage, but there are more differences than similarities, especially in the names of the ancestors nearest in time to Jesus, notably Joseph’s own father. Luke uses an elaborate story about a Roman census to explain the presence of Joseph and Mary in Bethlehem; Matthew gives the impression that they lived there permanently.
Then … Matthew recounts stories of a star, three wise men, and a massacre, while all Luke offers are a few simple shepherds inspired by angelic visions. In addition, where Matthew has Mary, Joseph, and Jesus fleeing from Bethlehem to Egypt in order to escape Herod’s death edict (2:13-14),Luke has them stay in Bethlehem for forty days and then return to Nazareth via Jerusalem (Luke 2:21-39). When Matthew brings them to Nazareth, it is (in keeping with his version of the birth story though at variance with all the other Gospels) as though they now go there for the first time (Matt 2:19-23) (Arnheim, 1984, p. 30).