Why do men button left over right and women right over left?

There is no definitive origin for this orientation.

This is a distinction that only predominated since the middle of the 19th century, when buttons became more widely used. Some theories date this from medieval combat where coat buttons were more easily undone with the left hand, but don't explain why women would require the opposite. A popular theory is that wealthy women were dressed by maids, but this would not explain the wide usage among all classes. The simplest explanation is that it was designed explicitly to define the gender that the clothing was designed for. Fashions for women tend to have an obvious distinction in their cut, so this would immediately suggest the gender for which they were intended.