Early scholars believed that prophets died on an anniversary of their birth.
Once they established Good Friday as either March 25 or April 6, they reasoned that Christ’s incarnation was nine months later, which would be either December 25 or January 6.
The choice was not simply to comply with pagan superstitions.
In 386 AD, when the date was established, any date would have collided with pagan rituals because they filled the calendar year.