One could write a book.
Basically, nobody knows when the historical personage whom we refer to as "Jesus Christ" was born. When the Romans adopted Christianity, they took their pre-existing feast of the Winter Solstice (Dec 21) and arbitrarily designated it as the "Nativity" - the day when God became Man.
The cultural phenomenon that we celebrate as Christmas has evolved in all Christian cultures, according to their own traditions. It is a fish-mash of different, sometimes contradictory aspects, not to be taken too seriously. The Christmas tree has nothing to do with the Nativity, and the giving of gifts would be more appropriate on the feast of the Epiphany (the "Free Kings," if you will). Santa Clause? Just a fanciful myth that was adopted from one or more European tales.
My own view is that "we" have two separate and distinct holidays on December 25th that should be celebrated separately. First is the Nativity, and second is the cultural holiday of Christmas. Only Christians should celebrate the former, but EVERYONE can celebrate the latter. Which is why Government employees get the day off.