Keeping students against their will perpetuates the myth that music lessons are painful drudgery and that being kept on by the teacher is a “mistreatment," as suggested above.
As students and performers ourselves, how many of us have perfectly sustained our high level of interest every day or every lesson since we started as children? Even as committed professionals, we still struggle with practicing, with keeping pieces alive for ourselves, with staying motivated when we’re tired or encounter obstacles. I don’t expect children to have this all figured out when career pianists are still dealing with it.
Also, how many people here were pushed into childhood activities for which we had no natural interest or ability? The resultant painful experiences: not pleasing a teacher or other adult, not fitting in, being forced to participate in sports, dance, academics etc beyond our ability to succeed, being kept away from the things we care about to satisfy what our parents care about. Is that what we want our studios to be about? Take the money and whatever happens, happens... as if a child’s interest and happiness were of no concern to us?
There are many levels of interest among our students. Occasionally the interest is so low that productive lessons are not possible. In that case, the parents have a responsibility to find a more fulfilling occupation for the child. And experienced teachers have a responsibility to let parents know that the lessons are not going to work. They rely on our professional judgment. If lessons continue, they may assume everything’s fine. But when a child reluctantly attends lessons with a teacher who in turn resents him, everything is not fine. By the way, it is unlikely that a teacher could harbor such disdain for a student as described in an above post without the student realizing it. Children have a pretty sharp radar about the adults they spend time with, especially one-on-one. If a low-interest student has a teacher who clearly resents and disrespects him, his interest is not going to blossom, and he’s certainly not going to practice more to please that teacher.
It is not reasonable to expect equal interest and investment from each student just because a parent signed him up for lessons. If we all had equally high desire to play the piano, nothing else would get done in the world. It is reasonable to expect this diversity, accept it graciously, keep the students who want to be with you, and tactfully free the others to pursue their real interests.
Lastly, it is always worth the effort to treat children well, even behind their backs.