Can someone that hates the government celebrate Independence day?
Can someone who doesn't? What would they be celebrating exactly?
There's a very strong case that America was founded on the idea that people do not need to be ruled. The founders seemed to believe deeply that if would be rulers can be sufficiently constrained, then the people can manage their own affairs, including systems of governance.
I love the same things you do about America, especially the idea that everyone gets a shot. A right to "the pursuit of happiness" is one of the most beautiful political sentiments I've ever seen.