And here's another article by Dr. Taylor Marshall from 2012 which explains what happened in the 4th century as a response to 3 objections. Fairly long, but worth reading for those interested in studying the history of the issue.
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https://taylormarshall.com/2012/12/yes-christ-was-really-born-on-december.html
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The Catholic Church, from at least the second century, has claimed that Christ was born on December 25. However, it is commonly alleged that our Lord Jesus Christ was not born on December 25. For the sake of simplicity, let us set out the usual objections to the date of December 25 and counter each of them.
Objection 1: December 25 was chosen in order to replace the pagan Roman festival of Saturnalia. Saturnalia was a popular winter festival and so the Catholic Church prudently substituted Christmas in its place.
Reply to Objection 1: Saturnalia commemorated the winter solstice. Yet the winter solstice falls on December 22. It is true that Saturnalia celebrations began as early as December 17 and extended till December 23. Still, the dates don’t match up.
Objection 2: December 25 was chosen to replace the pagan Roman holiday
Natalis Solis Invicti which means “Birthday of the Unconquered Sun.”
Reply to Objection 2: Let us examine first the cult of the Unconquered Sun. The Emperor Aurelian introduced the cult of the
Sol Invictus or
Unconquered Sunto Rome in A.D. 274. Aurelian found political traction with this cult, because his own name
Aurelianderives from the Latin word
aurora denoting “sunrise.” Coins reveal that Emperor Aurelian called himself the
Pontifex Solis or
Pontiff of the Sun. Thus, Aurelian simply accommodated a generic solar cult and identified his name with it at the end of the third century.
Most importantly, there is no historical record for a celebration
Natalis Sol Invictus on December 25 prior to A.D. 354. Within an illuminated manuscript for the year A.D. 354, there is an entry for December 25 reading “N INVICTI CM XXX.” Here N means “nativity.” INVICTI means “of the Unconquered.” CM signifies “circenses missus” or “games ordered.” The Roman numeral XXX equals thirty. Thus, the inscription means that thirty games were order for the nativity of the Unconquered for December 25th. Note that the word “sun” is not present. Moreover, the very same codex also lists “natus Christus in Betleem Iudeae” for the day of December 25. The phrase is translated as “birth of Christ in Bethlehem of Judea.”
The date of December 25th only became the “Birthday of the Unconquered Sun” under the Emperor Julian the Apostate. Julian the Apostate had been a Christian but who had apostatized and returned to Roman paganism. History reveals that it was the hateful former Christian Emperor that erected a pagan holiday on December 25. Think about that for a moment. What was he trying to replace?
These historical facts reveal that the Unconquered Sun was not likely a popular deity in the Roman Empire. The Roman people did not need to be weaned off of a so-called ancient holiday. Moreover, the tradition of a December 25th celebration does not find a place on the Roman calendar until after the Christianization of Rome. The “Birthday of the Unconquered Sun” holiday was scarcely traditional and hardly popular. Saturnalia (mentioned above) was much more popular, traditional, and fun. It seems, rather, that Julian the Apostate had attempted to introduce a pagan holiday in order to replace the Christian one!
Objection 3: Christ could not have been born in December since Saint Luke describes shepherds herding in the neighboring fields of Bethlehem. Shepherds do not herd during the winter. Thus, Christ was not born in winter.
Reply to Objection 3: Recall that Palestine is not England, Russia, or Alaska. Bethlehem is situated at the latitude of 31.7. My city of Dallas, Texas has the latitude of 32.8, and it’s still rather comfortable outside in December. As the great Cornelius a Lapide remarks during his lifetime, one could still see shepherds and sheep in the fields of Italy during late December, and Italy is at higher latitude than Bethlehem.
Now we move on to establishing the birthday of Christ from Sacred Scripture in two steps. The first step is to use Scripture to determine the birthday of Saint John the Baptist. The next step is using Saint John the Baptist’s birthday as the key for finding Christ’s birthday. We can discover that Christ was born in late December by observing first the time of year in which Saint Luke describes Saint Zacharias in the temple. This provides us with the approximate conception date of Saint John the Baptist. From there we can follow the chronology that Saint Luke gives, and that lands us at the end of December.
Saint Luke reports that Zacharias served in the “course of Abias” (Lk 1:5) which Scripture records as the eighth course among the twenty-four priestly courses (Neh 12:17). Each shift of priests served one week in the temple for two times each year. The course of Abias served during the eighth week and the thirty-second week in the annual cycle.[ii]However, when did the cycle of courses begin?
Josef Heinrich Friedlieb has convincingly established that the first priestly course of Jojarib was on duty during the destruction of Jerusalem on the ninth day of the Jewish month of Av.[iii]Thus the priestly course of Jojarib was on duty during the second week of Av. Consequently, the priestly course of Abias (the course of Saint Zacharias) was undoubtedly serving during the second week of the Jewish month of Tishri—the very week of the Day of Atonement on the tenth day of Tishri. In our calendar, the Day of Atonement would land anywhere from September 22 to October 8.
Zacharias and Elizabeth conceived John the Baptist immediately after Zacharias served his course. This entails that Saint John the Baptist would have been conceived somewhere around the end of September, placing John’s birth at the end of June, confirming the Catholic Church’s celebration of the Nativity of Saint John the Baptist on June 24.
The second-century Protoevangelium of Saint James also confirms a late September conception of the Baptist since the work depicts Saint Zacharias as High Priest and as entering the Holy of Holies—not merely the holy place with the altar of incense. This is a factual mistake because Zacharias was not the high priest, but one of the chief priests.[iv]Still, the Protoevangelium regards Zacharias as a high priest and this associates him with the Day of Atonement, which lands on the tenth day of the Hebrew month of Tishri (roughly the end of our September). Immediately after this entry into the temple and message of the Archangel Gabriel, Zacharias and Elizabeth conceive John the Baptist. Allowing for forty weeks of gestation, this places the birth of John the Baptist at the end of June—once again confirming the Catholic date for the Nativity of Saint John the Baptist on June 24.
The rest of the dating is rather simple. We read that just after the Immaculate Virgin Mary conceived Christ, she went to visit her cousin Elizabeth who was six months pregnant with John the Baptist. This means that John the Baptist was six months older that our Lord Jesus Christ (Lk 1:24-27, 36). If you add six months to June 24 you get December 24-25 as the birthday of Christ. Then, if you subtract nine months from December 25 you get that the Annunciation was March 25. All the dates match up perfectly. So then, if John the Baptist was conceived shortly after the Jewish Day of the Atonement, then the traditional Catholic dates are essentially correct. The birth of Christ would be about or on December 25.
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