A horse who refuses to pick up his hoof at your request is the picture of obstinacy. And an owner pulling and pushing to try to lift the immobile limb is the picture of frustration. To end foot-lifting battles once and for all, step back for a moment and consider why your horse may not want you to handle his hoof. Then make a plan to address the issue.
First, try to determine whether he is in pain. If he resists shifting his weight onto a foot, look for swelling or signs of injury in that leg. A developing abscess, injury or navicular syndrome may also cause resistance. If you find anything suspicious, call your veterinarian.
If you've ruled out pain as the problem, you're dealing with a behavioral issue. One solution is to retrain your horse to lift his leg on cue, which may involve brushing up on your own technique as well: On soft, level ground, stand next to his shoulder, facing his tail. Run your hand down his foreleg, and when you reach the chestnut, dig your fingertips into the leg just below it. Rub aggressively back and forth until his weight shifts to the opposite limb. The objective isn't to hurt your horse, but simply to annoy him to the point that he wants to move his leg to avoid the sensation.
It's important to instantly reward your horse by releasing your grip on the leg and praising him when he shifts his weight. Repeat this process on the same leg over the next few days until he begins to willingly lift it at your touch.
Once he lifts it, immediately set the hoof back down. Then gradually increase the length of time you hold up the leg, remembering that keeping the foot elevated for extended periods will seem like punishment to your horse.
After he is comfortable picking up the same hoof, you can move to the opposite side and start the process over. To work on the hind legs, grasp the base of the hock and rock the leg back and forth until his weight shifts over.