In common usage, “America” is short for “the United States of America.” It would be awkward to use such a long name every time you want to refer to the country. It’s as simple as that. Nothing to do with ethnocentricity or any other silliness.
And this is a usage that’s not only common in the U.S., but accepted all over the world. The fact that certain people (mostly Latin Americans) have a chip on their shoulder about this usage says more about their own insecurities and self-righteousness than anything else. People from other countries in the Americas of course have every right to call themselves Americans, but they shouldn’t be surprised when it just causes confusion.