March was not always the third month of the calendar. It used to be in first place.
With spring — the season of rebirth — occurring in March, that was good enough for the Romans and Saxons to place it first on the calendar. Even until 1752, the British considered March 26 the beginning of the legal year.
Since the month was so important to them, the Romans named it after a leading deity, Mars, their god of war. Now January comes first, named for Janus, the god of doors. Perhaps whoever was responsible felt January opened the door on a new year. How would Mars feel about that?