While Shepherds Watched Their Flocks by Night …
... all seated on the ground.
When exactly would shepherds do something like this? Turns out to be lambing season, late March, early April, when they have to be ready to help a ewe in distress 24/7. Not really anywhere near the time of the winter solstice (which WAS, however, celebrated by the Romans as Saturnalia and observed by the Zoroastrians as close to the day when their prophet died).
All those nativity scenes set in a stable? Where in the gospels does it mention a stable? Nowhere.
Remember the names of the 3 wise men (AKA kings or magi)? Caspar, Melchior, and Balthasar, right? Also never mentioned in the Bible.
Here's a couple of things that WERE mentioned in the Bible: the massacre of the innocents by Herod (in Matthew) and the worldwide census/tax ordered by Caesar Augustus (in Luke). Unfortunately for their credibility, that's the ONLY place they're mentioned, 1 gospel apiece. Neither the other 3 gospels nor any shred of contemporary evidence from other sources alludes to them at all.
How do we know that Jesus was fulfilling a prophecy? Because it says so right there in Matthew 1:22-25:
= = = = = =
 Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying,
 Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.
 Then Joseph being raised from sleep did as the angel of the Lord had bidden him, and took unto him his wife:
 And knew her not till she had brought forth her firstborn son: and he called his name JESUS.
= = = = = =
Yup, there you have it. Prophecy said they'd call him Emmanuel, and 2 verses later they up and call him Jesus. As clear a case of prophecy fulfillment as you'd ever want to ask for.
Why were Mary and Joseph in Bethlehem at all? Wasn't Jesus known as the Nazarene? Turns out that we have here a syncretistic melding of 2 traditions of a desperate captive people.
One tradition said that they'd be rescued by royalty, a descendant of their "great" King David (a lying, cheating, murdering, drunken philanderer, still living off his reputation as a high-school football hero who scored the winning touchdown over Team Philistia and their gargantuan defensive tackle Goliath). David’s city was Bethlehem. In order to establish Jesus's bona fides as a descendant of David, we get 2 different lineages, 1 each in Luke and Matthew, which have David as a starting point and Joseph as an ending point and not a single other intervening name in common. Nor are the number of generations the same. This tradition wanted Jesus associated with Bethlehem, "the city of David".
The other tradition said they'd be rescued by divinity, the "son of god" (such critters being a dime a dozen in the Mediterranean region of that era). In this tradition, it didn't matter squat that Joseph was descended from David, because Joseph wasn't Jesus's actual father. It was this tradition that wanted Jesus to be associated with Nazareth (a town which exists in modern Israel but which is depicted on exactly zero maps or lists of the Herodian era). It is widely assumed today that "Nazarene" means "resident of Nazareth", but it's not at all clear that that's what it meant at the time, since there apparently WAS no Nazareth.
So the fictioneers in charge of telling these stories had to figure out a way to make Jesus (a) both the direct son of God (and thus divine) as well as the direct son of Joseph (and thus heir to royal blood), and (b) a resident of both Nazareth and Bethlehem. They solved Problem A by just baldly claiming both conditions were true, evidently hoping nobody would notice (just as they figured nobody would notice the howling contradiction involving the prophesied name of the supposed savior). They solved the Problem B by dreaming up an excuse for the family to journey from Nazareth to Bethlehem.
Oh, and for another yuk, try to reconcile the differing accounts of where the family went AFTER Bethlehem.
Remember that all these stories were passed down solely by word of mouth for decades after Jesus's death. There seemed to be little point in taking the trouble to write them down, since he had promised he'd be back shortly, trailing clouds of glory and leading his dad's army of angels (the original embodiment of "shock and awe" tactics).
But, after half a century had gone by and the 2nd Coming was far more "awww" than "awe", a few anonymous scribes (known today as Matthew, Mark, Luke, and John, names just as accurate as Caspar, Melchior, and Balthasar) decided they'd better piece together the story as best they could from the oral traditions. And so they threw in everything but the kitchen sink, including all the contradictions.
Thus we inherited Xmas stories. Which would be perfectly OK as long as everybody recognized them for the fantasies they are. Unfortunately — Can you believe it in this day and age? — some people still actually think they're non-fiction.