Jesus’s birthday wasn’t December 25th – it was more likely sometime in September.
Jesus wasn’t born on December 25th. He wasn’t even born in the year 1 AD (AD, Anno Domini, a calendar system created entirely on the idea of the year of Jesus’s birth). There are competing theories as to why December 25th was chosen.
Christmas: meh ¯_(ツ)_/¯
To start, early Christians weren’t particularly focused on the date of Jesus’s birth – they were much more interested in Jesus’s ministry and Easter resurrection. The first recorded mention of Jesus’s birthday was around 200 CE by Clement of Alexandria who offered several possible dates, none of which were December 25th.
By around 300 CE two dates became associated with Jesus’s birth: December 25th and January 6th. December 25th became Jesus’s birthday for most western churches while January 6th became Christmas in a few others (January 6th also became the Feast of the Epiphany in western churches).
Despite what the internet might tell you, it is unlikely that December 25th was selected to usurp the pagan holidays of Sol Invictus, Saturnalia, or winter solstice festivals in general. Early Christians were strongly focused on distancing themselves and their beliefs from pagan religions. By the time Christians were co-opting pagan festivities to increase adoption of the faith the December 25th date for Christmas had already been established for over a hundred years.
From John the Baptist to Jesus
One of the best theories as to why we associate December 25th with Jesus’s birth has to do with the date of his crucifixion. There was a theory that great figures would be born and die in the same month (and even on the same date). The crucifixion has been calculated to have taken place on March 25th (but even that is debatable). Early Christians seem to have replaced his birth with his divine conception for this theory, and believing Jesus was conceived on March 25 (and counting 9 months later) brings us to his birth on December 25th.
So Jesus was born in December … except it could have been September. In Luke 1.26–27 we’re told that Mary was visited by the angel Gabriel in the 6th month of her cousin Elizabeth’s pregnancy. Elizabeth was pregnant with John the Baptist and, if we calculate his birth based on his father Zechariah’s priestly duties at the temple, John was most likely born in late March. If Jesus was conceived 6 months after John, and adding 9 months, then Jesus’s birth took place sometime in September. That said, this math could also work with Zechariah’s second time serving in the temple, which would then place Jesus’s birth around March.
Either spring or fall, these dates make more sense with the idea that shepherds would be out tending their flock (which the Christmas narrative tells us) – there aren’t a lot of shepherds out tending their flock in the cold of December. Further, it’s unlikely the census that Joseph and Mary traveled to Bethlehem for would have been in the winter, when the roads were in poor condition.