Today isn’t Jesus’ birthday, technically. It is just the day that we celebrate it. Historians believe His birthday is actually in March. Many other religions celebrate on January 6th, which seems to be the popular 2nd choice. How it came to be December 25th is because early Christians wished the date to coincide with the pagan Roman festival marking the “birthday of the unconquered sun”.
Oh, and Jesus wasn’t born in the year 0 either. Around 600 AD, a Roman monk named Dionysis was responsible for changing the calendar to pivot around the birth of Jesus. Unfortunately, Dionysis miscalculated the death of Herod by a few years and caused and offset in the calendar by about 4 years. I guess no one checked his math. Oops.
So the year is wrong and the day is wrong. It is just history — close enough. Merry Christmas!