The custom of mounting a horse from the left side has really nothing to do with the horse’s preference.
The custom probably began hundreds of years ago when men wore long swords on their belts. A man’s sword hung down his left leg, making it easier for him to pull it out quickly with his right hand.
Because of the sword’s position, it was easier for the rider to throw his right leg across the horse’s back. That way, the sword wouldn’t interfere with the rider’s leg as he mounted.
Even though riders today do not wear swords, the custom has lasted through the years, and when horses are trained, they are trained to accept riders mounting from the left. A rider mounting from the right could confuse or startle the animal.