It's actually much more complicated than that, and as someone who has been a student and is currently an adjunct professor, I find that attitude to be horrible.
The student-teacher relationship is a collaboration.
Also, please don't go through life thinking that every single person you might give money to for something is your "servant." Not even the person on the other side of the McDonald's counter.
I might buy that argument if the student and the professor shared the profits.
They don't.
Instead, the student is bound to pay every last cent of the education. Nowhere, other than court punishments and child support are debts protected against bankruptcy.
So yes, if I pay for it, I own it or I control it.
Edit: You misunderstand. I said servant, and I mean servant; not slave. Webster: "a person who is hired to do household or personal duties such as cleaning and cooking". Even the McDonalds cashier is that, when taking my order.
Unless your "professor" is actually a personal tutor you've hired individually rather than one many people -- that the institution can swap out without you having recourse -- working for an institution with which you are contracting for an array of educational services, you might have a point with your whole servant argument.
The student-teacher relationship is a collaboration.
Also, please don't go through life thinking that every single person you might give money to for something is your "servant." Not even the person on the other side of the McDonald's counter.