"Christmas" is NOT a Christian Holiday.
I know, it is confusing as fuck, thanks to the Roman Catholic Church.
The winter Solstice is a pagan holiday that has been celebrated in a variety of ways by various northern hemisphere sun-god religions throughout history.
The actual solstice occurs around December 21st. However, to anyone marking the location of the sun rise and set on the horizon from the perspective of a given spot, the sun doesn't begin to "return," that is, make its return journey northward, until December 25th. In other words, from that location the sun appears to rise and set at the same spots (more or less) for three consecutive days. On the forth, December 25th, it "rises" (as if from the dead) and is born (or re-born) for its journey northward.
January 1st is when the day's begin to become longer. (Due to the axis tilt of the Earth, there is a slight discrepancy between location of sun rise / set on the horizon and actual length of day.)
Anyway, the point is, these celestial events have been noted and recorded by humans for tens of thousands of years. Back in the "old days" 'science' and 'religion' weren't two separate classes of thought, they were identical. The sun was a god, an omnipotent being, about whom great tales were told -- it's annual journey of death and rebirth being one of them.
There is absolutely nothing in the Christian New Testament which indicates *when* baby Jesus was born, much less anything which says His birthday should be celebrated. It *does* say He is the "son of God". Somewhere along the way the early Catholic Church decided to sort of tie together the tale of Jesus's birth and resurrection with the Solar god traditions. SO… we got Christmas (winter solstice) and Easter (spring equinox).
Hope that helps.