Almost all teachers I had (piano, theory, singing) had the position: If you don't want the bread I'm selling you can leave. They were not my private teacher, they were payed by the state and also by me, by the taxes of citizen and my own money too. I was their client.
Could this be an arrogance that you find only among music teachers?
And when someone here was asking "why teachers insist of sheet reading?" this question was on hold because opinion based ...
"closed as primarily opinion-based!" I don't agree:This is not at all a opinion based question. It is absolutely evident that there are different types of learners (and this should not be depending of the teacher.) Therefore a discussion about the methods of teaching should be quite appropriate in this site. Richard has mentioned some important points. This question concerns students as well as teachers.
I also emphasize reading - by the way!