Christmas wasn't the birth of Christ. I am sure that everyone here has heard of Emperor Constantine, his vision, and Christianity's mark that was left on Western Civilization through him. Emperor Constantine was the first emperor to tolerate Christianity in his part of the Roman empire, then became a Chrsitian himself, and after taking over the whole empire, he declared Chrsitianity the official religion. Dec. 25 was actually a day that was put in place in honor of the sun god or something like that, one of the pagan gods of the Romans. It was basically the biggest day of the year in honor of a god. So he changed Dec. 25 to the celebration of the birth of Christ.
This might not be 100% right, but it is pretty close or it is what I remember from reading stuff.