I don't believe there is an exact date that anyone can say for certain that Jesus was born on, I did find this
The Exact Day of Jesus' Birth?
Therefore, according to the texts above we can approximate the month of Jesus’ birth to be around the time of Tishri (mid to late September). To arrive at this date, start at the conception of John the Baptist, Sivan (June), count forward six months to arrive at Gabriel’s announcement of the conception of Jesus, Kislev (December), then count forward nine months, the time it takes for human gestation, to reach Tishri (September), when Jesus was born.,
People I think just chose that date for who knows why,. If people celebrate Jesus birth that should be enough no matter the date,. If I'm not mistaken the people go to church on Sunday because it's the sabbath day but I'm pretty sure it lands on Saturday, I don't think that matters either as long as your giving worshipping Jesus.
It is my opinion, every body has one.
Love
Rick