Totally agree with what you say above. I want to add that while it's definitely an instructor/student relationship, it's also a provider/consumer relationship. Point being that it's not even as simple as one person being the teacher and the other is the student, though that's certainly part of it. But the student is paying for a service and the teacher is providing it. So, in some ways, the student is accountable to the teacher, but in some ways the teacher is accountable to his/her paying customer.
It drives me crazy when folks act like they're doing paying customers a favor by allowing them to learn their art. That's one manifestation of the crazy arrogance I referenced in an earlier response to
@Monkey Turned Wolf above.