To be fair, I think it is a bit confusing that the full name of this country is The United States of America, often just America for short, because of the whole thing with North America, South America, Central America, and Latin America. Basically all the countries in the west are part of <something> America, and the word "America" in that context has nothing to do with the name of our country (aside from being the same word and having the same origin).
I was fortunate to have a decent grade-school education wherein they carefully laid all of this out, with maps and stuff. And looking back, maybe it was pretty amazing that this was like Third Grade. Also, I'm one of those weirdos that likes learning stuff, and I thought it was pretty cool. I was never really surprised that some people get confused by it. I remember in junior high, I had to explain to someone that Texas and Florida are not in South America, but are in the Southern part of America. When you think about it, it is confusing.