It is a common myth today that the reason Christmas is celebrated on December 25 is because of a pagan feast for Sol Invictus that was celebrated Rome during the 3rd century. Actually, this is a quite a popular theory which is ironically rejected by a large consensus of current scholarship on Christian origins and Sol Invictus.
I've been doing a little reading on these issues and hope to make some more comments around here and reference sources. But for now, this is the best concise but clear essay I have found arguing against Dec 25th originating from Sol Invictus. The only thing that one could add is that if Christians had adopted the date for polemical reasons against the pagans, there were other feast days that were more important to Sol Invictus. The ever popular theory just doesn't stand up to scholarly scrutiny.
- Our first reference suggesting Dec. 25th was pagan in origin is from the 12th century.
- It is attested in the 3rd and 4th century that Christians connected Dec. 25 being 9 months after the death of Jesus (March 25) and connected the date of Jesus' conception to the date of his death.
- Even the Dontatists, who were zealous for maintain the purity of the church, held to this theory.
- The feast was celebrated on December 25 was held before Constantine made it official.
- While we do not have evidence as to the beliefs of the church fathers in the second and third century, we have clear evidence of how they ascertained the date in the 4th and 5th centuries.
Most of these details, and others, are affirmed by scholars of early Christianity and scholars of Roman religion. So for example, Hijmans in Sol: the Sun in the Art and Religions of Rome, argues that a later feast, relatively minor feast for Sol Invictus is more likely to been adopted by pagans as a polemic against a Christian feast rather than the other way around.
While there is more that can be said, I encourage to read the whole article. The author does not deny that Christians at times were unduly influenced by pagans and that influence encroached on the celebration of Christmas. But suffice it to say as to the status quaestionis most scholars now basically agree that December 25 was chosen as the celebration of the Lord's birth because it was nine month after the date we can ascertain for his death. The origins of a December 25th celebration are decidedly Christian and not pagan despite the popular mythology that abounds, largely in pop culture and anti-Christian mythos.