Why did the USA want to be separate from Britain?

Since this is in the World War 2 category, you may mean: "Why didn't the USA join the second world war at the same time Britain did?" Answer: The American public did not want their sons to die in a European war that didn't seem to have anything to do with them.

If you meant : "Why did the thirteen colonies leave British rule at the time of the War of Independence." Answer: "They didn't think it was fair to be taxed by Britain but not have any say about it in Parliament."