Exactly, imagine if people of the United States appropriated the name 'American'! I'm sure that every other country in the two Americas would be up in arms!

(It is a joke, laugh).

Some other countries actually use terms like United Statians or North Americans. And after traveling a bit makes the USA's use of 'America' seem arrogant or ignorant.

In italian "statunitense" is used, but probably not as often as "americano".

Canadians might still not be pleased about 'North American'.

I'm guessing you haven't traveled much. American is a virtually ubiquitous term to describe someone from the United States worldwide, no matter which language you're speaking. Countries which have a problem with calling yourself American are a minority, and even then it's usually a small minority of the younger generation.

If you go anywhere within Latin America, you'll find quite quickly that "American" is used to describe someone from the continents, and it's consider very odd to introduce yourself as "American" to a local. You say you're Estadounidense, or "Soy de Estados Unidos" (From the United States).

It's actually a very charged topic in Latin America, as many latinos feel that the word they use to describe themselves has been stolen.

I’m sure every other country with America in its name would be.

well, the complain was about calling Arabs the people from Saudi Arabia.

It was a bit of sarcasm, as it is exactly comparable. Go look at a globe and tell me which other countries have “America” in their name ;)