There seem to be several contradictions between Matthew and Luke in their relating the birth stories of Jesus.
MATTHEW says that an angel came in a dream to JOSEPH telling him his wife would give birth to Jesus. Then Jesus was born in Bethlehem, then WISE MEN came from the East following a star, and found Jesus at his HOME (in BETHLEHEM), then the angel appeared again to Joseph in a dream telling them to flee to EGYPT till the death of Herod. Joseph then headed back to Israel, but Archelaus was there, so they went instead and lived THEN in NAZARETH.
LUKE says the angel came to MARY in NAZARETH (where she lived) and told her she would give birth to Jesus, then Caesar Augustus decreed everyone be taxed and must go to the city of their lineage, so Joseph and Mary LEFT NAZARETH and went to Bethlehem, where Mary gave birth and laid him in a manger because there was nowhere for them to stay, then SHEPHERDS came. After purification, Joseph and Mary returned to their city of NAZARETH.
PLEASE EXPLAIN HOW YOU CAN HARMONIZE THESE DISCREPANCIES.
I have a very hard time seeing how people can find difficulty in harmonizing Matthew's and Luke's birth stories. They hardly overlap each other on any particular, other than in both of them telling us that Jesus' parents were Joseph and Mary, that He was born in Bethlehem and grew up in Nazareth.
Matthew tells the story from Joseph's side, and Luke from Mary's. It is a simple matter to intertwine them. My lectures on Matthew and Luke deal with the harmonization, which anyone really interested can listen to (they are free online). I will briefly list the events of the two accounts in chronological order:
1. Mary, in her home in Nazareth, receives a visit from an angel announcing that she will bear a child who will be the Messiah (Luke 1:26-38).
2. Mary decides to go visit her relative Elizabeth, whom she knows will believe her, because the older woman also experienced a miraculous pregnancy (Luke 1:39-55).
3. Mary returns to her home in Nazareth, three months pregnant (Luke 1:56).
4. Joseph hears of Mary's pregnancy, and contemplates breaking off the engagement. An angel tells him in a dream what the state of the case is, and urges him to go through with the marriage, so he does so (Matthew 1:18-23).
5. About six months later, due to a decree from Caesar Augustus, Mary and Joseph travel to Bethlehem, where the baby is born (Luke 2:1-7).
6. Shepherds visit the couple and the baby on the night of His birth (Luke 2:8-20).
7. The baby is circumcised on the eighth day, and dedicated in the temple on the fortieth day, according to normal Jewish practices (Luke 2:21-24).
8. At the baby's dedication, Simeon and Anna come and pay their respects to the child (Luke 2:25-38).
9. Mary and Joseph settle in Bethlehem—perhaps under the impression that the prophetic significance of the Messiah's birth there suggests that He should grow up there. While living there, when Jesus is a year or two old, they receive a visa from the wise men from the East who pay their respects (Matthew 2:1-12).
11. As a consequence of the wise men's visit, Herod seeks to kill the baby, but the family escapes to Egypt (Matthew 2:13-15).
12. Herod kills the male babies of Bethlehem, not knowing that the family of Jesus had already escaped to Egypt (Matthew 2:16-18)
13. After Herod dies, the family considers resettling in Bethlehem, but a warning from an angel not to do so causes them to return to their family home in Nazareth, where Jesus grew up (Matthew 2:19-23; Luke 2:39-40).
Where is the problem? I realize that getting all the facts sorted into their proper order requires that the curious person do a modicum of thinking about the material, but there is not the slightest difficulty in harmonizing the two accounts. The material exists in large chronological blocks. For existence, points #1—3 are one running, uninterrupted narrative, as are points #5-8 and #9-13. Only #4 needs to be inserted at the gap between Luke chapters 1 and 2, which is entirely natural.
I think skeptics do not wish very much to harmonize these accounts, since a child could do it (I did it when I was very young myself). They want to find difficulties, and do not want to find answers. This, more than anything in the material itself, explains their failure. It only requires a sympathetic reader, sufficiently interested in finding the harmony, to manage this.
The two assumptions that are gratuitously made by the critic in order to complicate things are:
• The assumption that Joseph's home (where he was in Matthew 1) was in Bethlehem (where he was in chapter two). This is not stated or implied in any passage. Nonetheless, one might have made this unwarranted assumption were we not supplied with the supplemental information from Luke that tells us of the trip that had to be made to Bethlehem. The fact that Luke 2:4 and 39 make it clear that Nazareth was their original home renders any suggestion that Joseph was from Bethlehem absurd.
• Luke 2:39 says: "So when they had performed all things according to the law of the Lord, they returned to Galilee, to their own city Nazareth." The critic's assumption (again, completely gratuitous) is that this return to Nazareth was immediately following the baby's dedication in the temple. Again, one might get this impression (though it is never stated in the text) if not for the supplementary account of Matthew, which places points #9-12 between the baby's dedication and the return to Nazareth.
Perhaps the stumbling block is in Luke 2:39 saying "when they had performed all things according to the law of the Lord, they returned to...Nazareth" There is no mention of a time period between the temple visit and the going to Nazareth. Neither is there any denial of such. The return of the family to Nazareth was indeed after "they had performed all things according to the law"—but this would be true whether they did so the same day, the next day, the next week, or some years later.
It is a commonplace for historical writers to pass over several years, in their narration, between one event and another. The gospels do this regularly. In the case before us, Matthew skips over about 25 years between chapters two and three. Luke skips over about eight years between 2:40 and 41. Then he skips over 18 more years between chapters two and three. Matthew, Mark and Luke all pass over several months to a year between the temptation of Jesus and the Galilean ministry (though John 1 through 4 fills-in much of that period). Such skipping simply represents the historian's selectivity in deciding what to include and what to leave out. There is nothing problematic about it. In the birth narratives of Matthew and Luke, both of them leave out many details, but the details each of them includes supplement the other's account.
An unbeliever may be excused for not having read or studied the Bible (though it seems very foolish not to do so, given the Bible’s foundational role in Western Civilization and in all education). There is less excuse for one criticizing what one has never studied and does not understand. It is outright disingenuous for one to study the Bible in order to create difficulties that do not exist, simply in order to discredit what one does not wish to find true.