This is a bit of a rant, but it’s something I hear from time to time that rather annoys me.
I first heard my seventh grade history teacher put forth the argument that the adjective “American” can never only apply to the United States of America but must apply to all of the continents of North and South America. I didn’t take issue with the argument then, but after continuing to hear it from a number of other people I’ve come to think that it’s stupid.
As stated, the name of the country is the “United States of America” or indeed simply “America,” so to refer to it’s people or culture as “American” is correct. Everyone should accept that it refers to a country and not a continent, if you say “American” to someone from Europe or Asia without a qualifier like North, South or Latin, they won’t imagine someone from Belize or Argentina.
Some people will insist that because there’s more than one country in North and South America, that people from America should be referred to as “from the United States.” However, the full name of Mexico is “Estados Unidos Mexicanos,” “Estados Unidos” meaning “United States” in Spanish. So if one were extremely anal they might reply to the statement “I’m from the United States” with “Which United States?”
To do so would be deliberately obtuse, but so is insisting that “America” must refer to both North and South America entirely. When we go against established conventions while speaking, we obfuscate our words and make communication much more difficult than it needs to be.