What a silly question.
People are commonly referred to by a derivative form of the name of the country from which they hail. The name of the country in question is The United States of America. Naturally, the derivative chosen was "American". It's not some sort of declaration of continental superiority, and it's not a slight to those in other countries on the American continents, it's simply a lot easier to say than "United Statesian" or "USA-ite". It's analogous to those from England referring to themselves as "British", when the British Isles technically include Ireland and Scotland as well.
Must everything be a conspiracy?