Because it is based on the solar calendar, there are none of the lunar uncertainties associated with many other pre-modern holidays. The specific solar date we know as December 25 can be found proposed in writings from the early 200’s. But, why did the eventual consensus settle on that date? Accounts vary, and it is a curious mystery. Nobody claims that the date was written on a Bethlehem birth certificate. There is no such document, and if there had been, the date would have been expressed as a lunar date from the ancient Jewish calendar. I think our solar date is equal parts historic reconstruction, arbitrary convention, and high art.
The best web page I’ve seen on the origin of the December 25 date for Christmas is this one by David Bennett. Bennett recounts several plausible theories, and debunks some popular ones, notably that ancient Christians somehow shot themselves in the foot by co-opting one or more pagan holidays.
Bennett’s article describes two biblical lines of evidence (known of course to the ancients) that indicate that Mary became pregnant some time in March. This underlies the traditional celebration of the Annunciation on March 25. Add nine months gestation, and you get the traditional celebration of Jesus birth.
Apart from historical truth, I think it is fitting in these days to remember that the historic Church has reckoned the Incarnation as beginning at Christ’s conception, even though the most visible celebration of it is tied to his birth. The respect Christians have for the unborn Christ (which is biblical: see Elizabeth’s greeting to Mary) is no small part of the Church’s traditional aversion to abortion.
I personally incline toward William Tighe’s theory that the early Church assigned the Annunciation date to the conventional estimate of Jesus’ death date, March 25. (The ancients were trying unsuccessfully to refer to the historic Passover date; see Tighe’s Touchstone article.) This is all conventional, but when data is lacking, a celebration requires some such convention. It’s not a stretch given that real historical data places the Annunciation some time in March, and the Crucifixion some time in March or April.
Doubly identified with both conception and crucifixion, March 25 can prompt both deep sorrow and great joy. A few years ago when Easter fell near March 25, a Catholic Eastern Rite liturgy I went to recognized Jesus’ incarnation and death in one remembrance. It was powerful. My point here is that a proper understanding of Christmas in the calendar points not only back to the Annunciation but also forward to the Crucifixion. As some carols point out, the little Babe was born to die.
In any case, given the conventional meaning of March 25, December 25 is a simple corollary, and the proximity to the winter solstice is not man’s invention but a humanly unintended consequence. If so, the link of Christmas to the rebirth of the Sun, like that of Easter to the festival of Passover, is best understood as a creative flourish of divine poetry.