My daughter is not musical, but is an artist. She now attends an Arts High School here in MN...The Perpich Center for Arts Education. They have 5 areas of arts...Theater, Music, Literary Arts, Media Arts and Visual Arts (my daughters area). Much of the 300 students in grades 11 and 12 are VERY talented. The kids go thru quite a process to get into the school and many of them dorm there (its only for MN residents) and live away from their families. Quite a few of them come from small communities, so it is a HUGE change for them. The school is right outside of Minneapolis proper. These kids and parents are already putting themselves in a critical position and pressure filled place to succeed and excel in their areas just during the application process for this place. For my child, it is THE PERFECT place for her, as compared to her regular high school environment. This is the case for many of these kids.
As far as my own child's Art and getting criticized, etc....she enters art shows/contest with some regularity now as the request and pushing of teachers. There is judging and failure and also great success. And remember, art, singing, etc, is a very subjective thing for people to judge and offer opinions on. Not everyone likes the same thing! But I am not going to hold my child back, if she wants the experience (and my child is very inward and sensitive, cries easily, not assertive, etc), I support her every inch of the way.
If during a process of judging, etc, my child were to say ENOUGH...I would say OK, we are done. Why wouldn't I? I sure would try to reason with her, calm her down, see what set it off and see if we can get thru it. But if quitting is what will keep her emotionally healthy, I would support that too.
How is this different than those "mainstream" kids who play sports, parents push them and don't let them quit before a big game or whatever...theres pressure and criticism, etc....