I dont know all the details, but I do know this Adam though he was punished as the days got shorter, On December 21 He saw the days started to get longer again and realized he was forgiven.
He then celebrated December 21 as a holiday, It became an avodah zorah holiday celebrated for a week
Fast forward a few thousand years. followers of a new persecuted religion wanted to celebrate the birth of their savior which was forbidden in Rome.
As Romans were celebrating the december 21st holiday which actually lasted about a week, The followers of the savior decided to celebrate the birth at the same time. The normal Romans would think they were just celebrating solistice and not think anything of it.
So actually December 25 is actually related to Adom Harishon