Afraid you're wrong about that one unless your pony has been accustomed to being mounted from both sides. Yes the etiology of the left side mount has to do with swords and where the tack and cinch buckles, but some horses are going to have their say about what's "traditional" just to them alone. I've even seen an old work mare that would shy and sidestep if you tried to get on from a fence rail on her right side. Needed to see the process out of the left eye. They also don't like the rear approach. No prey animal does.

jack