I do think competition is good, but . . . when I was at school I enjoyed tennis, rounders, gym, but never excelled at any of them and so was never amongst the first choice to be in any teams (just for playing during lessons, I didn't stand a cat-in-hell's chance of ever being selected for competitions!), which was quite demoralising.
My one advantage was that, being left-handed, I used to earn loads of points for 'no balls' being hurled at me by either a racquet or bowler, plus it meant that when I did manage to whack the ball hard no-one was prepared for the direction it was heading, so when the pickers cottoned on to that it meant that at least I wasn't the last player to be chosen!! 
I agree with Flickety that perhaps more emphasis should be placed on a child's personal triumphs rather than simply winning/losing, after all there will be some children who will never win no matter how hard they try.
Yes, that's one of life's lessons, sometimes one has to accept one's limitations without developing a complex about it, however harsh it seems!