The ultimate reason for the envy of all British children (as well as those from a lot of other countries) is that American children don’t have to wear a uniform. There are some private schools which require uniforms, but mainly students over here can wear what they like, within reason. They can express themselves every day through their outfits.
The rules aren’t quite as lax as it might seem from the outside, though, as there are things you’re not allowed to wear. These vary between schools, but often involve strappy tops, too short skirts, or ripped jeans.