Why do men's clothes have buttons on the right while women's clothes have buttons on the left?

I always wondered why men's clothes have buttons on the right while women's clothes have buttons on the left.
When buttons were invented, they were very expensive and worn primarily by the rich. Since most people are right-handed, it is easier to push buttons on the right through holes on the left. Because wealthy women were dressed by maids, dressmakers put the buttons on the maid's right! And that's where women's buttons have remained since.