Semantics. Although the label "American" can be used to describe any resident of the continents of North and South America, it has traditionally and legally been used to exclusively describe a citizen of the United States of America. That's the context in which I used the term.
If one considers the citizens of the Confederate States to have remained Americans, then one is forced to admit that the so-called War Between the States was in fact a civil war between Americans. And that admission raises all sorts of interesting questions.
You simply can't have it both ways.