It's definitely not Dec 25th....there is at least 3 other ancient religions that observed there "god's" birthday on dec 25th...scholars think this is because the 21st-24th are the 3 darkest days of the year and starting on the 25th it gets lighter and lighter everyday..supposed to be a sign of light during dark times!!
Nobody really knows the exact day of his birth. The first century Christians did not even celebrate birthdays, because of their deep ancient pagan roots, and Jesus never command his disciples to celebrate his birth. I don't think Jesus would even condone this lie, or half truth birthday celebration.
The story goes that Joseph and Mary were going to Jerusalem to be counted for the census,roman writings from that time period indicate this was done sometime in the months of June and July, Jesus was born during this trip