They are trained now to canter in the arena?! That's odd. That's where people should be learning to canter. Learning in a larger field can be dangerous... There is LOTS of room to pick up speed.
You horse probably doesn't want to canter because you are leaning forward, your hands a flopping all over and your not balanced. Also, your stirrups are pretty short, I'd let them down easily two holes. I think its nice to give a student a taste of what a canter is like in a controlled environment to give them a fighting chance if something happens. If you were mine we'd be going to no stirrups, no hands, pole work and posting patterns. All these will help steady your hands and improve your balance.
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