Did Jesus's family flee to Egypt, or go home to Nazareth? Matthew 2 vs Luke 2

The passages

When he arose, he took the young child and his mother by night, and departed into Egypt.

Matthew 2:14

And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.

Luke 2:39

The problem

Matthew places Joseph and Mary in Bethlehem as if it were home. They flee to Egypt, and only after Herod's death does the family settle in Nazareth, because Joseph feared Archelaus in Judea. Luke has them in Nazareth beforehand, traveling to Bethlehem for the census, and going back to Nazareth after the presentation at the Temple, forty days after the birth. There is no room for Egypt in Luke's account, and Matthew never mentions the census.

What believers and scholars say

Luke omits. Defenders point out that Luke 2:39 says only that they returned to Nazareth after the Temple rites. It does not say how soon, and the Egyptian trip could fit later in the account, in the time before Luke's next scene at age twelve. Gospel writers do skip material.

Different stories, same core. Brown and many others note that the two infancy narratives share very little apart from the birth in Bethlehem, a virgin mother, Joseph and Mary, and the name Jesus. They conclude the accounts come from separate traditions, and that each author shaped his material for his own purpose. Matthew's story echoes Moses (a wicked king, a massacre of infants, a flight and a return), which suggests that the shape is theological.

Matthew's Egyptian episode may have a scriptural root. The Hosea quotation in Matthew 2:15 ("Out of Egypt have I called my son") seems to have prompted the Egypt story as much as the other way round. Some argue this means the story was built from the quotation. Others say the quotation was chosen because the events had happened.

Where this leaves it

A harmony is possible if Egypt is placed after the Temple visit and the return to Nazareth comes later than Luke implies. It requires moving Luke's sentence away from its plain meaning. Whether that is acceptable depends on how much you expect two writers to coordinate. The two accounts mostly do not try to.