If this were a horse of mine in training, I would stick with the task of working with his legs all day long until he became relaxed and comfortable. But first, I would groom him thoroughly, as this not only relaxes the horse very much, but gives you an idea of sensitivities he may have other than what is going on with his feet, which might even have a direct link to a possible issue he is having somewhere else. It could be that he is just not accustomed to anyone working with him in this way. It's possible that whenever he lifted his leg, it seemed to the handler that he was going to kick, and so it was given up on, and he learned to act this way when his legs are approached and now he uses it to his advantage.
Many horses will try to be helpful and actually lift their leg to assist you in reaching for it. In some horses, it even seems like they are "kicking out" or jumping around, but it's because they are lifting their own weight, and if you don't reach for it with confidence and in time, they will have to put it down quickly, also making that seem like an aggressive act, but it's not at all.
What I would suggest that you do is work with him on the ground by doing things like grooming, and even exercising him enough to get him very relaxed. Then, hose him off, making sure to focus a lot on his legs. This will all help towards "desensitizing" his legs a little more. Then, take him back to his stall, tie him if if he ties, and then start working with picking his feet out starting with one side at a time. For example; the left front, then the left hind, then the right hind and finally the righ front. Once you and your horse learn the routine of going around in a circle like this, he will learn to balance himself and even anticipate your next move, which will assist you in picking up his feet.
When you going to pick his feet, make sure to "cup" the whole hoof mostly towards the toe (for leverage)- in your hand firmly, and don't let go, even if he tries to pull away or rebalance. This moment is crucial for him to learn that he cannot evade. If you are not sufficiently supporting the hoof, he may find all sorts of ways to hop out of your grasp. Also, remember when working with the back legs, horses tend to pick up there legs awkwardly, so you have to reach for the hoof and then allow the horse to drop his leg comfortably. Sometimes they will jerk their legs, or even stretch their leg straight out behind them. Some will even hold their leg curled up tight under their belly. As long as the horses hoof is in your hand, continue confidently picking the foot out as if nothing is going on. Repeat walking around in the circle I mentioned earlier on all four legs until your horse learns the routine.
From what you are saying, it really seems that your horse just needs a confident handler to help him through his confusion and mistrust. Work with him at least once or twice every day with this. Keep in mind, you need to see his hoof regardless, because if there is a chance there is something wrong with his foot, it will need to be addressed....hope that helps :) Let us know how things progress