They shouldn't have to be required to excercise. Exercise should be fun for kids, they should want to play and move around. But since they don't want to do things that are healthy and exercise anymore, they should be required to exercise so they can grow up to become healthy adults.
Yes, exercise is an important part of education for children. Childhood obesity is a growing problem that is exacerbated by sedative lifestyles. Requiring exercise in the schools is imperative for keeping children healthy, especially when they might not be getting enough exercise at home. It also helps children develop healthy habits, so that they will hopefully continue to exercise as adults.
Children need physical exercise, whether it comes in the form of sports, gym classes, playing outdoors or taking dancing or gymnastics lessons. Sedentary lifestyles lead to obesity and poor physical health, which compromises immunity to diseases and creates health issues early in life. Parents and schools share the responsibility for ensuring that children participate in healthy, physical activities.
Humans, children and adults alike, own their bodies. As free thinking human beings, children and parents have the capacity to choose how they treat their own bodies. In the United States, the constitution prevents the government from regulating how a citizen maintains it's own body. It should stay this way and other governments should follow this example.