1. IF a Jewish boy is born on Dec. 25, his bris would be on Jan. 1, and the goyim hold that someone important to them was a Jewish boy born on Dec. 25. Of course, even according to their scholars, “Dec. 25” is a myth based on a Roman holiday (Saturnalia).
2. For a long time the “new year” in the Christian calendar began on March 25 (at least in English speaking countries), and the change to Jan. 1 was not motivated by religion but by a desire to standardize calendars.