As a piano teacher myself, I just want to comment on how sad I feel that so many people seem to have had such poor experiences with teachers.
I believe it's just hard in general, and in any field, to find a teacher that is a good fit. There's certainly the element of experience and ability to inspire (which, I think, is a trait rather than something that can easily be learned; people, somehow, pick up on whether someone is genuine or not), as well as competence on the subject that they teach, but a large part, I feel, is just a matter of individual chemistry.
Looking back at my school time (I went to quite a few due to moving and other reasons), there were only a handful of teachers who managed to kindle lasting enthusiasm in me. It was easier for those who taught subjects that interested me (the "talk-y" kind of subjects, like religion, history, sociology), and harder for those who were unfortunate enough to be tasked to teach me something about math, physics and other entirely too logical things.
I did have one physics teacher who made an impression, and I don't even know why. He was an older, rather disillusioned teacher, but, and I think that made all the difference, he listened. He was interested in my opinions, even though physics left me cold (in fact, we spent most of the time discussing the stock market, which I was super interested in when I was sixteen and broke; by the time I had income and could have applied my knowledge, I was naturally no longer interested!). In turn, that made me want to learn from him, and my grades improved.
It was, though, for the most part, solely a matter of compatible personalities and mutual respect. I also never
felt criticized by that teacher, even when he did, which I think was of tremendous importance to me as a somewhat troubled teenager who didn't feel like he fit anywhere, which presumably many teenagers experience. Delivering criticism without making the recipient feel "defensive" is an art.
I have a lot of respect for teachers who care, and who continue to care even when they are not always, or only rarely, appreciated. I think the lack of appreciation is very pronounced especially in public schools. Perhaps caring goes hand in hand with having a "mission", wanting to make a difference, rather than just doing the job they get paid for. Then again, that probably applies to many professions.