You never know when you might have no choice but mount from the “off-side” of your horse. You could be out on the trail and a cliff is to the left side of your horse, or some other hazard or injury that prevents you from mounting or dismounting from the left side of your horse.
It’s pretty easy to practice mounting and dismounting from both sides of your horse. You can start by practicing at home with a kitchen or dining room table chair. The back of the chair becomes the front of your horse. To mount, practice swinging your right leg over the chair and sitting softly onto the chair. Now practice from the other side by swinging your left leg over the chair. Reverse the motion for dismounts. Once you get pretty good you can mount one side and dismount the chair from the other side. Practicing this motion on a chair helps build muscle memory in a safe environment before you add your horse and other outside factors that may make practicing more difficult. Plus, if you accidentally kick the chair, your chair isn’t going to scoot out from underneath you.
Now that you have the movement down by practicing with your chair, you can start to practice with your horse. It is helpful if your horse is patient and will stand still while you practice. Locate a tall mounting block to help you. Do the same exercise you did with your chair with your horse and the mounting block. As you build comfort and confidence, gradually reduce the height of your mounting block until eventually you are practicing from the ground.
Having this skill will prove invaluable when you actually need it, and you’ll be glad you took the time to practice.
Note: always mounting from the ground pulls on your horse’s spine and withers. Over time this can cause asymmetry in your horse’s spine and possibly pain. It is best to mount from a mounting block as it reduces the strain on your horse’s back. When I ride, I mount from one side and then dismount from the opposite side so there is balance in the movement on my horse’s back.