An objective look shows that many traditions supposedly rooted in the Bible don't match the biblical account.
Did three wise men travel to see Jesus? The Bible doesn't say how many there were. There could have been more. We are told only that they gave Jesus three kinds of gifts: "gold, frankincense, and myrrh" (Matthew 2:1-11). Did everyone exchange gifts when Christ was born? Gifts were presented to Jesus because He was born "King of the Jews" (Matthew 2:2, Matthew 2:11). This was the expected custom when appearing before a king, thus the wise men brought gifts fit for a king: gold and valuable spices. Jesus alone was the recipient of the gifts; others did not exchange gifts among themselves.
Did the wise men, as nativity scenes often depict, arrive to find Jesus in a stable manger, there having been "no room in the inn"? (Luke 2:7). No. When the wise men arrived, apparently some time after Christ's birth, Joseph's family was residing in a house (Matthew 2:11).
Did the writers of the four Gospels (Matthew, Mark, Luke and John) consider Jesus' birth to be one of the most significant events for Christians to acknowledge or celebrate? Mark and John do not even mention the event. Although Matthew and Luke do, neither gives the date. None of the biblical writers says anything about commemorating Christ's birth.
Did Jesus Christ tell us to celebrate His birth? No. He left explicit instructions regarding how His followers are to commemorate His death (1 Corinthians 11:23-26), but nothing about His birth.