Why is it offensive to call the U.S. Dollar “American money”?

My thought process is that it's called the United States of America, so I say "American" money. Just as I might say something like Canadian money or Mexican money if I couldn't think of/didn't know the proper name of the currencies. Two separate people I've talked to thought this was offensive, as it implies that other countries in the continent of the Americas aren't American. But from this explanation I still can't really see why, can someone explain? I genuinely don’t know the answer.