A video would be interesting!

Along the lines of several posters who talked about green horses not cantering well, my mare came to me having been taught NOT to canter - she was a harness horse. Sure she could run around the field with her friends, but she could barely canter six strides on the lunge line without losing her balance and falling into the circle or falling into a really fast trot. We didn't start riding the canter until she could canter a couple circles on the lunge with her head down in a relaxed position and staying nicely on the circle. It took months.
It was really helpful to us to work on more complex stuff at the trot before starting to canter with a rider - first we made sure she could trot long and brisk, and then also collect up a bit and trot a smaller circle, do slow-faster-slow-faster transitions, patterns like figure eights and serpentines of different sizes, etc. Then when we worked on the canter with the rider a) she already knew the word "canter" from the lunge work and b) she had really developed good muscles and balance in her hind end and back to make it easy to take off into a controlled canter instead of flipping inside out and doing a mad trot. Green horses can't always get a canter if they are not set up to push off with the hindquarters, and if he's falling through the corners/cutting corners, then he's not balanced and he's probably got too much weight on his forehand, which will make it really hard for him to get his feet organized for the canter.

So it's possible (even though your guy has a different background, or maybe is just being a pig) that if you develop more of his skills at the trot first, then come back to the canter gradually, you can "re-teach" him how to canter properly and in a relaxed way, and break this pattern where he gets agitated and annoyed and anxious about the canter. I think it's never a bad idea with horses to back up a spend more time on something more basic if he's struggling. No matter what the cause (ignorance, confusion, or obnoxiousness) he'll benefit from you patiently setting him up to win, rather than getting mad at him for failing (which might just make him more anxious, and thus more prone to fail or try to evade.)

Hope that makes sense.