I agree that forced competition can be damaging.
But I also agree with Quinlan that learning to exercise is just as important as learning how to work abstract problems. (The only reason working problems is given more emphasis in school is because it makes more money. Further development of technology, etc. People are forgetting the importance of other things!)
That's why gym classes should hold options like running laps or working in the fitness center. Personally, I hated gym in my elementary days because people just got so... serious about a game. I remember a semi-un-athletic girl in my class who did a really good serve in volleyball, but the teacher made a HUGE deal about her being 2 steps in front of the stupid line.
I think gym should put emphasis on competing with yourself and your best time, not raging bloody murder on the other team. Giving people a common enemy is NOT the same as natural teamwork!
I hadn't realized the difference until I started taking martial arts in middle school, and by then I had already ruined my health a fair amount, having assumed that exercise meant misguided competition. Still regret that very much today. :[
And those who can't teach... teach gym!