You should be able to mount your horse from either side and from any position. When you do ranch work, it is not always convenient to climb on your horse in the traditional manner. There are times that mounting from a fence, rock, truck or other place is needed. You may have a calf or tool to carry in the saddle with you that is hard to hold while you climb aboard. It is simpler to slide over with the load and avoid trying to mount with it.
Small children are another good example. When really small, it’s not real hard to get in the saddle while holding them. As they grow and get heavier, it is more convenient to have them stand on the back of the tailgate and slide into the saddle. Some people have knee issues from illnesses or injuries and don’t need the aggravation of the joint with the full weight of their body in the stirrup.
We teach our horses to stand still while you get on or off whether on the tailgate or nearly any other place. It just makes sense for the horse to let the rider mount from more than just the left side in the customary way.