America is the whole continent, period
If "America" refers to the USA country only, or to the North American Continent, how to call the South American Continent? Is like if USA could be used to refers to the whole USA OR only to the State of New York. People from other States simply wouldn't accept it.
I can easely understand that is easier to say "America" instead of "the States" or "U.S.A" or "United States of America". But this is simply wrong.
Germans don't call Germany "Europe" (in fact they call it "Deutschland"), Sicilians don't call their island "Italy" (they call it "Sicilia"), people from the Republic of South Africa don't call their State "Africa" (they call it "South Africa") and citizen of the United States of Mexico call their State Mexico and call themselfs Mexicans.
Probably the problem is that "United States of America" is not a well conceived name for a country, and I can understand, after inventing names for 51 States it was difficult to invent a name representing them all, when the cohesion between them was not at all an evidence.
This is not the fault of US citizens. It's just a historical/cultural/language problem. As you probably know, most of Central and South America citizen feels Americans, they belong to the American Continent, and they're proud of it. When they call themself "Americans they think about the whole continent (it would be strange, for them, to feel Americans in the sense of US citizens no?), but they don't like at all that "America" and "American" means, for a very large part of the world (European citizens, like me, in primis) only the U.S.A and the US citizens. It is not fair.
I had the same problem. Hopefully a friend of mine, an American from Mexico, insisted on change my linguistic/cultural habit. Now in my head "America" refers to the whole continent, and "Americans" to its citizen. All of them.
for more see: America is not a country
for a more or less accurate discussion see wikipedia: http://en2.wikipedia.org/wiki/Wikipedia_talk:Manual_of_Style_(US_vs_American)