Well, you are right about why it *started* as being that side... it was the sword thing. So we just stick to that side. Horses are very one-sided. The hemispheres in the horse's brain are not connected as they are in humans, and this means if he accepts actions on the left side of his body, it does not necessarily mean he will accept them on the right side of his body, as to him it is two totally different actions. So we have standardized the left side as the side the horse is trained for everything, from haltering to leading to mounting. The horse really doesn't care which side you start on, but horses like consistency. Most riders and stables train their horses to be mounted from the left, so that's why people still stick with that side. There's nothing saying you couldn't teach the horse to be mounted from the right side as well as the left... we're just lazy. :) However, you wouldn't want to try it on a horse you don't know, as yes, some horses would freak out.

-Leen