Wow that just sucks! I say its not you at all, its the instructor. You're there to learn how to ride, not to learn how to fall off, and the instructor sees how Obie is. She shouldn't allow training riders on the horse until its fully rideable and doesn't try to throw riders off.

I say talk to your instructor, whoever it is doesn't sound all too responsible to me. Good luck, I hope you can get a horse that won't try and make you fall. Cause riding can be soo amazing if you have the right horse