[molotovh]

In this case, it's because the teacher is now left not knowing whether they have an opening in their schedule for the student or not.

This is a freelance teacher who is responsible for finding her own clients and managing her own schedule. If you let them know that you won't be taking any more lessons, they can find another student. If you lie to them and they think you'll be back for your lesson next week, they aren't going to look for another student to fill your time slot. So when you don't show up, you've just cost them to opportunity to earn money from someone else.

If I were in the same situation, I would absolutely institute a policy of continuing to bill for the student's time slot until they formally cancel services. Given the level of conflict avoidance being practiced here, I foresee such a policy being quite profitable.

[atemerev]

I assume they have paid in advance already, as I inferred from text. And yes, of course, everyone bills until formal cancellation, at least here in Switzerland.