Are you alone or in a group when this happens? I learned more etiquette today. I learned when riding with others that you make your horse stand still until everyone is mounted and secure. If one horse moves, they all will, resulting in a potential rider injury.
Silly, I know. Common sense when it is actually spoken but to the newbie...
If you are alone, might you find another rider for practice sessions? Someone whose horse can stand still and lead by example?
If you are in a group, think about the other horses and if they are being still or not. Maybe one is too close?
During lessons, my trainer mounts my horse and makes him stand. His first steps are always backwards, before forwards. Stand. Back 2-3 steps. Stand. Then go forward.
While mounting, if my horse moved forward he dismounted the stirruped foot and had the horse work back and into a whoa (stand).
This is a training issue. Horses don't know to stand. If, in the past, you mounted and immediately moved or body cued the horse to move, he is only responding to that training.