A post at Psephizo, entitled "Why do Matthew and Luke offer different birth narratives?" is well written and names a number of important issues in the reconciliation (if possible) and differentiation of the two accounts.
Overall, it makes an excellent case for each writer composing a story to express a viewpoint; and its weakness is that it offers no grounds for thinking that either account is anchored in history = what actually happened.
A specific weakness, in all accounting for the historiography of Matthew and Luke's early chapters, are their difficult-to-reconcile accounts of the reason why Nazareth becomes the place of Jesus' upbringing: in Matthew, Nazareth is a refuge from Herod in Judea; in Luke, Nazareth is the home already for the holy family, who only leave it for the purpose of the census and its requirement that they respond to it in Bethlehem itself. And that matter is scarcely touched on in this particular account at Psephizo.
The other day my association with Academia (a kind of mega academic articles repository, here is one you might like because we spotted your interest in that subject, store and alert thingy) led to an email promoting "The Birth of Jesus: The Evolution of Jesus in the Infancy Narratives" by William S Abruzzi. It is quite a long article but its thesis is simple:
"Numerous stories about the birth of Jesus were written during the first several centuries. When considered as a group, they tell us more about the evolution of early Christian beliefs about Jesus than they do about his actual birth."
The opening sentences set out an approach unlikely to be found in many pulpits this Christmas, or in books published by, say, IVP or Paternoster Press:
"Every year at Christmastime, millions of Christians throughout the world hear these words from Luke's gospel. They also hear stories of three Wise Men traveling from the East to pay homage to the newborn "King of the Jews;" of shepherds "tending their flocks in the field;" of a star shining over the place of Jesus' birth in Bethlehem; of visits by angels; of warnings given in dreams; of the massacre of innocent children by the evil King Herod in his attempt to kill the infant Jesus; and of Joseph, Jesus' earthly father, taking his family to Egypt in order to escape Herod's wrath. While these tales provide a beautiful prelude to opening gifts under the Christmas tree, none of them is true. They are all fables. Indeed, the modern version of the Christmas tale is a synthesis of several independent stories merged into two distinct and contradictory infancy narratives presented in the opening chapters of the Gospels of Matthew and Luke. Most Christians are completely unaware of the inherent contradictions presented by the two infancy narratives."
I certainly agree that in many churches in Aotearoa New Zealand, an annual "Christmas pageant" service (perhaps held yesterday, the Sunday nearest the middle of December) will have been a "synthesis" of Matthew and Luke: wise kings and shepherds appearing on the same night before the Infant King.
I am not so sure about boldly declaring of Matthew's and Luke's accounts (included along with other Infancy Narratives), "They are all fables." Such a declaration assumes we know what didn't happen as well as not knowing what did happen.
Matthew and Luke agree on certain things: Joseph and Mary are the earthly parents of Jesus; Jesus is conceived in the womb of Mary without human sexual intercourse taking place; the birth takes place in Bethlehem, when Herod the Great is (local) ruler of Palestine/Israel, and the upbringing of Jesus takes place in Nazareth.
Matthew and Luke tell different stories from one another: as we all know, there are wise kings in Matthew and not in Luke; shepherds in Luke and not in Matthew; a threat from Herod which drives the Holy Family to temporary refuge in Egypt according to Matthew and unmentioned in Luke. Notably, Matthew gives us Joseph's encounters with God's divine messages whereas Luke gives us Mary's encounters with God's divine messages. None of these differences are necessarily contradictory.
The most obvious contradiction (in my view) between Matthew and Luke is how they report the Holy Family arriving in Nazareth.
Luke has a natural sequence, with not a hint of a shadow of a threat of persecution by Herod, in which birth is followed by circumcision, followed by presentation in the Temple, followed by return to Nazareth, warranted because "they had finished everything required by the law of the Lord" (Luke 2:39). Further Nazareth has been Jospeh and Mary's home and so the journey to Nazareth is a return home.
Matthew has a different natural sequence which takes the Holy Family to Nazareth, and that journey is not a "return home" but the making of a new home: fear of Herod's persecution leads to the journey to Egypt; Herod's death leads to the possibility of return to Judea; but a new Herod ruling over Judea leads to a decision to head to Galilee, in which district lies Nazareth where the new home is made (Matthew 2:19-23).
We can only speculate what sources (if any!) Matthew and Luke each have in order to arrive at such differences in the telling of the birth and infancy of Jesus.
Here I am interested in the theological considerations which drive Matthew and Luke, as well as Mrk and John to their respective versions of the beginnings of Jesus' life, whatever their sources may have been.
Matthew, to begin with the first of our canonical gospels, tells a story of Jesus as a new Moses. The first Moses was threatened with infanticide at the decree of a king, though the king was Pharoah and the location of the threat was Egypt and not Judea (Exodus 1-2). Moses is protected through refuge in a basket and then a hidden life in the court of Pharoah himself. The second Moses is protected through refuge in Egypt. But Matthew is also telling the story of Jesus as a new Abraham (see the genealogy in Matthew 1) and a new David (so the prophecy from Micah associated with Bethlehem as the place of Jesus' birth, Matthew 2:6). Through story, Matthew sets out the theological (or christological) significance of the baby Jesus in relation to the story of the people of God known as Israel: fathered by Abraham, taught by Moses and ruled by David.
Mark, most likely written before Matthew and Luke, doesn't bother with any details about Jesus' birth (though he tells his story as the story of a man with a family, since they appear at certain points). Theologically, he sees no need to underline Abrahamic, Mosaic or Davidic qualities of Jesus. Everything Mark wants us to know about Jesus is found and emphasised in Jesus' preaching and miracle working or in his encounters with religious authorities. There is no back story to Mark's Jesus: just the front story of Jesus the preacher, power worker and provocateur.
Luke, whether he knows of Matthew's Gospel or not, seems disinterested in Jesus as the new Moses, but he is very interested in Jesus in relation to the Roman Empire (so the big driver in his story of Jesus' birth, Luke 2, is an imperial census which draws the Holy Family from Nazareth to Bethlehem; later, in Luke 3, the beginning of Jesus' adult ministry is set very precisely in terms of "the fifteenth year of the reign of Emperor Tiberius"). For Luke, the kingdom of God is both an alternative to the kingdom of Rome and not a rival to the kingdom of Rome (a theme in Acts). Theologically, Luke's Jesus is a new and greater Caesar/Lord, who also fulfils a number of Israelite prophecies - hopes and aspirations for a new and better day. Thus, the presentation in the Temple, at the end of Luke's story of the young infant Jesus, is less about fulfilling legal requirements and much more about Anna and Simeon's joy at seeing the fulfilment of their hopes and aspirations. Fittingly, for Luke's Jesus as an ideal human ruler of a world kingdom of gentleness and compassion, his version of Jesus' genealogy goes past Abraham to Adam himself.
John, whatever his knowledge of Matthew, Mark and Luke, is, like Mark, disinterested in details of Jesus' conception, birth and infancy. But somewhat like Matthew and Luke, John is interested in the ultimate origins of Jesus. A new Moses? Descended from Abraham? Adam? Ok, says John, but let's go further and deeper: Jesus is the Word present before time began; Jesus is the only Begotten Son who comes from the Father's heart. Christmas is all very well as a festival of birth but why have such a limited celebration when we could celebrate Jesus as the agent of creation itself? (So, John 1:1-18).
Wonderfully, each of Matthew, Mark, Luke and John is agreed on one thing: Jesus is the Son of God!
And each says that in quite different ways: Matthew 2:15; Mark 1:1; Luke 1:35; 2:49; 3:38; John 1:18, 34.
Theology by narration!