Well, I don’t believe he was ever born. I don’t believe a man named Jesus Christ ever walked on the face of the Earth. There is no historical record of his birth (or even his existence) outside the Bible, despite the Romans being meticulous record keepers. That said, in the unlikely event he was ever born, there’s absolutely no evidence whatsoever to indicate this even took place on December 25.
Here is one explanation of the date choice. I don’t know enough about the history cited to have an opinion on its merits.
At this time, the emperor Aurelian established an official holiday called " Sol Invicti " –
meaning unconquered sun, in honor of the Syrian sun god “Sol,” and also in honor of
himself, since the emperors were regarded as the divine incarnation of Apollo. This
holiday was held on December 24 and 25. And it more or less established December 25
as the official solstice. All other religions that worshipped sun gods also accepted
December 25 as a fixed date for their celebrations. And the major festivals of the
Egyptian earth-mother Isis were held on December 25, January 6, and March 5. The
earliest Christians assumed that Christ was born and was resurrected on the same day –
March 25 – which was assumed to be the vernal equinox. Later Christians celebrated the
birth of Christ on January 6, along with the festival of Isis. By the fourth century, many
Christians were referring to December 25 as the day of the “unconquered son” – in
defiance of the emperor, and January 6 was then called “Epiphany,” when either the
magi were supposed to have visited or Christ was baptized, or maybe both.