Here are some popular traditional beliefs compared to what the Bible/history says:
Belief: Jesus was born on December 25th.
Reality: The Bible doesn't state the date; it was chosen later much later, possibly to coincide with pagan festivals or based on Mary's conception date. Shepherds tending flocks in fields occurs in spring/early summer, not winter.
Belief: There were three Wise Men (Magi).
Reality: The Bible doesn't specify a number; the "three" comes from the three gifts (gold, frankincense, myrrh). They weren't kings. more likely astrologers, and probably arrived much later, not the night of the birth.
Belief: Jesus was born in a stable/barn because the inn was full.
Reality: The "inn" was likely a family home and they couldn't get the guest room, so Mary gave birth in the main family room where animals might also be kept. The manger was a food trough for animals.
Belief: Mary and Joseph arrived the night Jesus was born.
Reality: Luke's Gospel implies they were in Bethlehem for the census, and the birth happened sometime later, not necessarily immediately upon arrival.
Belief: Jesus was an only child.
Reality: The Bible mentions Jesus having brothers and sisters, pointing out that he wasn't an only child. Historians suggest that Mary had other children after Jesus, or they were Joseph's from a previous marriage.