Willis tracks the Christian observance of December 25 to the Donatists, a bunch of hard-liners if ever there was one. They make, Willis suggests, an unlikely group to introduce a pagan custom into their high demand community.
After much research, the church in the West and Africa settled on March 25 as the date of Jesus' crucifixion. This was important in determining the date of Jesus' birth because in Jewish tradition it was thought that prophets died on the same day as they were born. This idea may seem strange to us, but was understood and accepted by the early church. Jesus was different from the prophets, however -- his life didn't start at his birth, rather it began when the angel spoke to Mary. This is why early Christians celebrated the annunciation (or announcement to Mary that she was carrying the child) on March 25. Add nine months of pregnancy and you arrive at a birth date of December 25... we should understand that it is not a pagan festival "borrowed" by Christians. Rather, it is a very early Christian memorial.