Had this happen, my daughter had this happen. Best guess is every new rider has experienced this. I understand you want to get it right but bouncing on the horses back and continuing to cue only causes pain and frustration. You are balanced on a finely built suspension bridge under which sit the kidneys. Would you like to be pounded in the back? Another thing that is happening is you are also teaching the horse this cue means you don't have to canter. Your instructor put another person on to tune up the horse and get it responsive to the leg. Lessons are never about how far you go but more about fine tuning things and *always* allowing your mount to do it right before lesson's end.
If you are going to be an effective rider or competitive rider, you are going to have to swallow your pride and learn to shake it off. The idea is for you to watch the other rider and see how they apply the aids. Our brains learn by watching as well as doing. Watch as many CDs of top riders as you can and ask questions. Meanwhile, I would apologize to the instructor and ask what you can do to improve the canter depart.
Don't be frustrated and remember it's a dance, not a boxing match.
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