Okay, this is more of a possible explanation than a hard fact.
Have you ever wondered why men and women’s shirts button on different sides? No? Me neither… I actually didn’t even know that they buttoned on different sides until about 5 minutes ago.
But now that I’ve been made aware of this, I’m demanding an explanation! The Straight Dope gives us a totally random possible answer- breastfeeding, of course.
During the time that buttoned garments were being designed, women would always breastfeed with their left breast. Apparently, they also would always protect their babies by covering them with the right side of the dress or coat. This is why the buttons were positioned for women (right-over-left) to make life a bit easier for the nursing mothers.
And men simply got left-to-right buttoning because that is what is easiest for right-handed people.
Alternative explanation: In medieval times women were dressed by their maids- almost all of whom would have been right-handed.