A trainer. That's my tip. My guess is timidity when picking out his back feet taught him he could avoid it by wiggling his foot, which built into kicking. Don't tie him close enough to a fence that he could kick it while you're cleaning his back feet.
For bridling, ask him to lower his head by placing one hand at the poll, the other on the bridge of his nose. Place pressure at the poll while moving his face back and forth with the hand on his face. Release when he drops his head, let him lift it back up. Leave him alone if he leaves it down, keep asking him to drop it after he picks it up, until your touch at his poll makes him drop his head. Take him to a round pen, make sure you can touch his ears, poll, neck, everything, both sides. If he doesn't stay with you, send him of in the round pen and make him work his tush. Ask him to come back in and try again. He'll soon learn he can either work his booty off, or stand and rest with you in the middle. He'll be more inclined to let you touch anything. Then, with those two tools, you can start to work on bridling.
'He doesn't rear, he just jerks his head until you move it away'
He's training you. ;) and you're training him to jerk his head when you bridle. He jerks his head, you move it away. You're releasing the pressure for the wrong reaction. That release of pressure is reinforcing the behavior. Don't ask for anything you can't finish, because you can't stop once you've started. Whatever he is doing when you release the pressure is what he'll be more inclined to do next time you apply that pressure. Does that all make sense?