Biblical Archaeology Review has a good scholarly discussion of why Christmas is celebrated on December 25. And it is evidently NOT because it was superimposed on a pagan holiday:

The most loudly touted theory about the origins of the Christmas date(s) is that it was borrowed from pagan celebrations. The Romans had their mid-winter Saturnalia festival in late December; barbarian peoples of northern and western Europe kept holidays at similar times. To top it off, in 274 C.E., the Roman emperor Aurelian established a feast of the birth of Sol Invictus (the Unconquered Sun), on December 25. Christmas, the argument goes, is really a spin-off from these pagan solar festivals. According to this theory, early Christians deliberately chose these dates to encourage the spread of Christmas and Christianity throughout the Roman world: If Christmas looked like a pagan holiday, more pagans would be open to both the holiday and the God whose birth it celebrated.

Despite its popularity today, this theory of Christmas’s origins has its problems. It is not found in any ancient Christian writings, for one thing. Christian authors of the time do note a connection between the solstice and Jesus’ birth: The church father Ambrose (c. 339–397), for example, described Christ as the true sun, who outshone the fallen gods of the old order. But early Christian writers never hint at any recent calendrical engineering; they clearly don’t think the date was chosen by the church. Rather they see the coincidence as a providential sign, as natural proof that God had selected Jesus over the false pagan gods.

It’s not until the 12th century that we find the first suggestion that Jesus’ birth celebration was deliberately set at the time of pagan feasts. A marginal note on a manuscript of the writings of the Syriac biblical commentator Dionysius bar-Salibi states that in ancient times the Christmas holiday was actually shifted from January 6 to December 25 so that it fell on the same date as the pagan Sol Invictus holiday.5 In the 18th and 19th centuries, Bible scholars spurred on by the new study of comparative religions latched on to this idea.6 They claimed that because the early Christians didn’t know when Jesus was born, they simply assimilated the pagan solstice festival for their own purposes, claiming it as the time of the Messiah’s birth and celebrating it accordingly. . . .

There are problems with this popular theory, however, as many scholars recognize. Most significantly, the first mention of a date for Christmas (c. 200) and the earliest celebrations that we know about (c. 250–300) come in a period when Christians were not borrowing heavily from pagan traditions of such an obvious character. . . . In the first few centuries C.E., the persecuted Christian minority was greatly concerned with distancing itself from the larger, public pagan religious observances, such as sacrifices, games and holidays. This was still true as late as the violent persecutions of the Christians conducted by the Roman emperor Diocletian between 303 and 312 C.E. . . . .

There is another way to account for the origins of Christmas on December 25: Strange as it may seem, the key to dating Jesus’ birth may lie in the dating of Jesus’ death at Passover. This view was first suggested to the modern world by French scholar Louis Duchesne in the early 20th century and fully developed by American Thomas Talley in more recent years.8 But they were certainly not the first to note a connection between the traditional date of Jesus’ death and his birth.

Around 200 C.E. Tertullian of Carthage reported the calculation that the 14th of Nisan (the day of the crucifixion according to the Gospel of John) in the year Jesus diedc was equivalent to March 25 in the Roman (solar) calendar.9 March 25 is, of course, nine months before December 25; it was later recognized as the Feast of the Annunciation—the commemoration of Jesus’ conception.10 Thus, Jesus was believed to have been conceived and crucified on the same day of the year. Exactly nine months later, Jesus was born, on December 25.d

This idea appears in an anonymous Christian treatise titled On Solstices and Equinoxes, which appears to come from fourth-century North Africa. The treatise states: “Therefore our Lord was conceived on the eighth of the kalends of April in the month of March [March 25], which is the day of the passion of the Lord and of his conception. For on that day he was conceived on the same he suffered.”11 Based on this, the treatise dates Jesus’ birth to the winter solstice.

The article goes on to document other ancient sources that associate the day of Jesus’s conception with the day of His death, going back to rabbinic Jewish texts that make similar connections.