It may be safe to assume that the exact day and year Jesus was born didn't matter to the people who knew and followed him because they were there. And when it eventually was decided to be important by the early Church as the bishops chose from literally hundreds of stories about Jesus and which to decide were sacred, an important day had to be chosen. No coincidence that December 25th was chosen- right at the end of the popular pagan festival of Saturnalia and three days after the winter solstice to tie back to Jesus' three days in the tomb, as many of the stories claimed. The number three is important in many religions throughout the world, so why not choose the third day after Saturnalia? It helped tie together the diverse stories told about Jesus, at least the ones the early (can I say "pagan", since that's what it was and still is) Church accepted, with much revision, and considered "true".