Some of the mounting left (as in your left foot stays on the ground the longest, and you swing your right leg over) comes from horse calvary days. Most soldiers were trained right handed, so your sword hangs on the left. Which means when you're mounting a horse with your sword banging around on the left, it is FAR easier to swing your right leg up and over.

(ahhh the fun trivia one learns when one's other hobby involves medieval history)