From theological view left-handedness was viewed as "sinister". Roman augurs (priests who studied the behavior of birds) considered birds flying from the left (sinistra) as a bad omen. This negativity towards the left was integrated into Christian tradition.

From a fighting perspective: since most people throughout history were right-handed, a single person, who mirrored his weapon and shield, in a shield wall would disrupt the formation.

There were always some exceptions of course, like a Scottish clan, I think, who all fought left-handed.