Is he enjoying his rides? That’s something you need to look for. I know my horse, when I first got him, he stayed pretty much completely still when I got on him (and this is a 16.1 hand horse, with no mounting block, in an english saddle, clobbering my way up on top of him) but a little while after I got him, he started moving when I tried to get on him. This, along with some other behavior problems he had started to develop, was a hint that he wasn’t enjoying his rides (turns out we were asking more than he could understand at the time). As pheets said, horses always have a reason for what they do, and a lot of the time, not letting you get on means he isn’t enjoying what you’re doing when you do get on him. So, check for that, try to keep arena work interesting, challenging, and different each time. Also, it could be that when you do get on him, you immediately ask him to move forward. Horses will begin to anticipate this, and start to move off before you even get on, because they’re anticipating that that’s what you’re going to ask them to do, so they just automatically do it. So when you get on, make sure you don’t immediately ask him to move, but ask him to stand still for a minute, then move off. As far as fixing the problem, (you may need to do this without the mounting block) gather your reins up, so they’re tight, but not pulling on his mouth. Act like you’re going to get on, and as soon as he starts to move, apply a light pressure on his mouth, not yanking him backwards, but just lightly asking him to give his mouth and take a step back. If he doesn’t respond, increase the pressure until he does. But the second he takes a step back and isn’t fighting you by pulling back on the bit, immediately release him, give him a pat, and do it again until he stands still for you to get on. If he moves off when you get on, immediately back him up a step or two.
I’ve just started doing this with my horse, and granted he’s an unbelievably fast learner, but with doing this three times he’s already getting the point to stand still when I get on and I only have to ask him to back up once before he stands still, and he doesn’t move off when I get on anymore.