I too believe, Lagin, that you're the student. You could have asked as a student and not written as if you were a teacher. I doubt answers you recieved would have been different, and you would have had the opportunity to be more honest.
How would you react if that same student decided they didn't want to compete any more? It would depend the reasons I would hypethetically be requiring competition. I require my students to perform in a recital or they cannot be in my studio. I require the older students to participate in a solo festival of some sort (solo and ensemble, or a competition). The reason I require it is so students can have and understand the experience of performing under pressure. It's valuable for students to know how to perform in this environment. Not only for musical reasons but because we all have to perform under pressure in life. It's life practice. Also, many competitions give not only places and "winners" but feedback from the judges. This is the best reason to send a student into a competition; so they can get feedback from other professional musicians and perhaps gain more insite to their playing via a different opinion. Other teachers may require their students to compete and push them to win if they know the student plans on a performance degree at a university -- then the teacher would be RIGHT to push the student very hard. If a student is going to be noticed by symphonies, or world famous teacher, that student is going to be competing and winning competitions.
Therefore, if one of my students told me they didn't want to compete anymore, I would tell them it was a requirement of my studio and explain why. The student could be HONEST and explain right to my face why they didn't want to compete. If it was merely a battle of wills and they were going to have a fit or be stubborn I would tell them they could find a new teacher, best student or not. Taking lessons is not only about loving music. It's about learning and accepting the responsibility of what comes with a particular teacher's expectations. This would of course be very painful for me, but that's how it is.
For a student who can bring a teacher much acclaim by winning all the time, how would you feel? If a teacher is using a student like a grand champion dog in shows, that's wrong. However, it's just as wrong of a student to assume this is what the teacher is doing. The teacher may have a motive for sending students to competitions that they havn't communicated to the student very well. The student should talk to the teacher and find out what the teachers main motivation for encouraging competitions is.
Would you still enjoy working with that student as much, if they're practice habits were excellant, or would it be tainted in that you could no longer "live out your dream" through them? Teachers don't "live out their dreams" through their student. Washed up performers "live out their dreams" through their students, not teachers. Again, don't assume that's what's happening, if you are indeed the student. And if you are the teacher (which I doubt), you ought to check yourself and reasess why you teacher.
My advice:
1. Talk to your teacher about how you feel. Be HONEST.
2. Ask them why competitions and winning are so important to them.
3. Share with your teacher what your plans are for music in your life -- hobby, teaching, composing, performance, etc.
4. Ask other music teachers if the reasons you were given for competition are good ones, if you're not sure.
5. Find a new teacher if your present teacher only pushes you to live vicariously through you or baske in the glory of a successful student (but only after you did 1, 2 and 3.)