I am a bit concerned over any pain the horse may be experiencing. It is a bit of a red flag when the horse has one particular limb or sore spot that he is defensive over.
My thoughts exactly. When you said he was only picking up three feet, I was wondering why he wouldn't let you have the other one.
My gelding used to be fussy when we picked up the left front foot. Then, he got a quarter crack on his left front foot. Most people would have the farrier/vet look at the front left foot... but we had them focus on the front RIGHT foot. And sure enough.. that's where the problem was.
He was compensating all his weight on the front left, so when we went to pick it up to pick it, he would hate it, because it would put all his weight on his front right foot.. the ouchie one. He then got a split on his front left foot, because he was putting all of his weight of his front end on his front left foot.. and it finally cracked.
So, sometimes the problems are a bit sneakier to figure out ;)
And as for getting him to pick up his feet better.. the way I train the babies, is to pick the foot up and hold it for a moment. I wait until they stop wiggling, and as soon as they stop, I count to three, and put the foot down. Don't be too ambitious! Don't expect to clean his hoof out on the first attempt. Let him know when he stops wiggling, his foot will be put back down.
I notice this post is kinda old.. I hope all is going well! And since its a back leg, beware being kicked! =)