During the first few centuries A.D. there were many estimates by ancient scholars as to when Jesus was born, but none of them put it on December 25th. The main reason why Jesus' birth was celebrated in Rome on the 25th of December was because it's the final day of the pagan solstice holiday of Saturnalia. Since Christians were often persecuted at the time, it was convenient for them to honor the birth of Jesus during the solstice holiday so that they wouldn't stand out among the celebrating populace and be persecuted. The tradition stuck even after Rome converted to Christianity, since the Roman populace didn't want to give up celebrating their most important holiday. In reality, we really don't know when he was born, and scripture only dates the Nativity relative to other Biblical events of which the exact dates are also still unknown.