About three weeks ago my instructor told me to get off. We were riding in the indoor and my horse made a move to kick a passing horse. I got off the horse and my instructor got on. She rode him for about 10 minutes and schooled him. After my mount was responding better my instructor had me get back on. She then explained to me what she had done and how I should respond.
I was a bit embarrassed but then I realized I am there to learn and that I can't let pride get in the way. My instructor had handled it well and I learned something. Your instructor was right for taking you off. I just think she should have explained why so you wouldn't be feeling like this.
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It sounds like it stopped being a lesson for you though. There should have been explanation about what the person that got on after you was doing so in the future you will have the facilities to correct your own horse.
My riding group loves when our trainer hops on--it's nice to have someone else fight a battle, for one, and it's so cool to watch someone you enjoy learning from in action.
Another thing that probably would've happened at our barn, especially so early on in the lesson time, was to have you saddle up on another school horse.