Try shortening you rein on the side you are going to mount (near side )
But to be a safe horse your horse must be taught to stand while you mount , check girth, adjust stirrups , paint your nails , fix you hair hahaha
opps getting carried away here .
But really the horse should stand until you ask the horse to move . Im big on obediance
Keeps us safe . And every time you handle / ride you are teaching the horse something good or something he will try out again which is not so good .
One reason horses may not stand is if their saddle dosnt fit and is uncomfortable when mounted . or The horse is sore somewhere associated with riding. Check it out who knows .