Please help with my horse! ?

One major difference between canter/gallop and all other gaits is that the horse's spine is always bending in the direction of the lead he's on.  In any other gait, his spine is straight.  (Bending side to side, not up and down.)  Therefore, it's most likely that the problem is that your horse is just too stiff through the spine to go on a smaller circle.

To fix this, start to improve his spine flexability with exercises to supple it.  At the walk, do a circle he's comfortable with, and start spiralling it inwards so it's smaller and smaller.  Make sure his spine bends to match the arc of the circle - support his inside shoulder with your leg at the girth, and push his hind end into the curve with your outside leg a few inches behind the girth - or more if that helps.  Use your inside rein only enough to direct him, while supporting with the outside rein so he can't just turn his head, he has to bend his body.  This will take time and practice for both of you.  Be sure to do it equally in both directions.

Then, when you know what you're looking for and how to get it, do the exercise at the canter.  Put him into a slow canter around the perimeter, then gradually spiral into a smaller circle.  Make sure he's on the right lead (counter canter is difficult and not what you want) and wrap him around your inside leg, supporting the curve with that outside rein.  KEEP THAT ARC around the circle through his body!

It's also helpful to do lots of turns at the walk, making sure he bends his spine into the curve, not just his legs and neck.

Look up other exercises for suppling on line.

This will no doubt take time.  It's possible he's stiff in the spine for physical reasons, so that vet visit is appropriate before you start.

Good Luck with him!

The really good, successful barrel/pole riders make sure their horse is trained slowly at a walk, then trot etc to navigate the obstacles long before they are asked to speed.  Bending the body, responding to leg, rein and seat cues.  They don't just take the average horse out and expect it to be fast.

Go back to the beginning and work with this poor horse at the WALK and then the TROT.  Make sure your cues are correct.  I know it's a bore but you have a horse that is a regular saddle horse and you should have bought a trained barrel racer.

He should be kept in his own inclosure. He is a danger to other people's horses/pets. I had a horse that you could not put him in with most horses, only mares or babies. He would round up the herd and sort out the ones he hated, I had to do something and put him in his own paddock. Good Luck!

Like you said it could be something physical, but why is it important that the horse canter in circles if he doesn't want to for whatever reason? Maybe he would like to do something else.

This sounds stupid but have the vet also check the horses eyes.  With one of my mares she had managed to injure her eye bad enough that the interior lens had been scratched bad enough that it left a scar in the lens as well as the outer cornea.  She was seeing double of things according to the vet and she got spooky only on her left.  

When we put a fly mask on her and covered only the eye on the side with the old injury she went along just fine.  It took her a few weeks to get used to the mask being on while I rode her but she finally stopped bolting and refusing to go on trails or near barrels etc,

Besides pain from the mouth, teeth etc it could possibly be a visual thing, rare but does happen.  Let the vet do a whole health check, a pinch in the back, spinal problem, arthritis etc of a joint or even a hoof problem could cause a behavioral issue.

Have you tried with both being tacked up and totally free of everything except the halter?   Sometimes the hardware the horse wears can be an issue such as the saddle pinching her when your mounted or maybe something else punches or rubs when she turns another direction.

Good luck.