You want them to become successful, to achieve the excellence of which they're capable. You want them to have loving and supportive relationships. And you want them to enjoy themselves. These are fine goals. Competition is to self-esteem as sugar is to teeth.
Most people lose in most competitive encounters, and it's obvious why that causes self-doubt.
Success comes to be defined as victory, even though these are really two very different things. Kyle had been used to winning ever since a tennis racket was put in his hands at the age of two. But at the very end of the show, someone in the audience asked him how he felt when he lost. This is not to say that children shouldn't learn discipline and tenacity, that they shouldn't be encouraged to succeed or even have a nodding acquaintance with failure. When classrooms and playing fields are based on cooperation rather than competition, children feel better about themselves.