I guess I'll be the dissenting opinion on this one, both as a student pilot and as an experienced private teacher in another profession.
If you are teaching as your profession, meaning you are being paid to teach, the expectation that you should enjoy and cherish every moment with every student is unrealistic. You are being paid.. you are working. As a friend of mine was fond of saying to his son (who kept quitting jobs because they "weren't fun"), "That's why they call it WORK!! If it was fun, they wouldn't pay you to do it, and everyone would be doing it!" I've had thousands of students over my career, but admittedly only thirty or so privately. Speaking only of the private students, I was always clear with my expectations out front just so they wouldn't waste their money, but never turned anyone away if I had an opening or time available nor required an interview or application. The students that didn't prepare for lessons weren't near as enjoyable as the ones that did, but I still got paid and life went on. The students that showed up unprepared week after week after week couldn't really enjoy their lessons anyway, so they always eventually quit. That's fine, too, but I wasn't about to give up on anyone. It was always their decision.
As a student, and this may very well say more about my personality and thoughts than it would a prospective teacher, if I had a CFI or teacher of another subject want to interview me first to see if I was worthy of their expertise, I'd be so turned off by that attitude that I'd feel that teacher wasn't worthy of me as a student. In my lifetime, I've had some remarkably unskilled, handicapped-by-everything-life-can-throw-a-person students who were nightmares to teach for a while that, for whatever reasons, had some switch flip and ended up being some of my favorite, most life-affirming influences in my time on this planet. The thought that I may have missed out because at one time I deemed them unworthy of my time is both humbling and sobering.
Sooo.. as a teacher, I give every student willing to pay me for my help a chance, without question. Those who show true interest and effort over the long term, I tend to repay with extra effort myself. As a student, I expect the same from my teachers.