First, teach the horse to 'stand' no matter what you are doing with him. It is best for the horse to stand square. This is when he is most balanced. If the horse is not square when you pick up his foot, he is not well-balanced enough, and may even be leaning as if he was just going to walk off, but you are holding his foot when his weight shifts to that part of his body to walk, so he can either back up and panic and be even more off balance, or lean into the weight where his leg would go, but then falls.
A lot of times, we have to restart from baby steps in the beginning. First, I think he needs to learn and understand how to properly shift his weight to other feet while you hold on. If you want to pick up his left front hoof, all his weight should be on his right hind foot. Take a rope and just apply pressure to the back of his fetlock with it on his front foot, to start there first. As soon as you feel his weight shift off of that foot, release pressure. That's what he was supposed to do, keep weight off that foot.
But first, he needs to learn to stand still, and as square as you can get him so he is well balanced.
Lettin' the cat outta the bag is a whole lot easier than puttin' it back. -- Unkown