Actually, I did not say that everyone who lives on the two American continents is an American. I merely stated that the term is sometimes (inappropriately, in my opinion) applied to everyone in North and South America. I further stated that the term "American" has been traditonally and legally applied exclusively to those people who are citizens of the United States of America. In my opinion, anyone who renounces his United States citizenship and transfers his allegiance to a foreign government ceases to be an American. However, if he subsequently takes an oath of allegiance to the United States, then he is once again an American.
If one chooses to believe that being an American is a function of geographical proximity rather than a right of citizenship, then the term "Mexican-American War" is, indeed, a misnomer. In fact, adhering to that belief while simultaneously calling one's country the United States of America is truly arrogant and insulting to all the other "American" states on the two continents which are not included in the United States.