The Department of Education asserts that "Americans" includes Mexicans, Canadians and others in the Western Hemisphere, so referring to U.S. residents as Americans is inappropriate. In the department's view, "America" happens to include South, Central and North America. Accordingly, when referring to the colonial period, the state bureaucracy requires teachers to refer to "the colonies of North America" or "North Americans." After the American Revolution, the nation is called the United States (not of America).OK, I see what they are doing here. Someone got the bug in their keester that they needed to be "non-offensive" about how we are described to the outside world. I.E. we wouldn't want to go around offending anyone by saying that we're Americans and you're not, even though you live on the North American continent.
So I thought I would offer some thought from a geographer's point of view. First of all, trying to narrow the name of this country down to just the United States (even though it's common enough to do so) is not technically correct. You don't call the People's Republic of China just "the People's Republic." America is part of the name and has been from the beginning. In fact there are more countries in the world than you can count on your hands and feet with longer full names than just the Democratic Republic of the Congo, or the Federal Republic of Germany, or the People's Republic of Bangladesh. It's just that you don't see those titles every day like you do with the United States of America.
So for purely formal reasons it makes sense that people refer to this as "America" as it is the short form of the country's name.
Now from the point of arguing that because the continent's name is America, we can't specifically refer to ourselves as "Americans." There are areas in the world where a country's name takes on the name of the region, or the continent. The Congo is a region of central Africa, but one country that contains most of it gets the name. South Africa is the name of a country, as well as the southern region of the African Continent, which includes more than just that country.
Australia is a country and a continent.
Also, if they are trying to be politically correct about not offending anyone, I don't think that you'll go anywhere in this world where when people say "Americans" they aren't talking about us. Not the Mexicans (heck the Mexicans probably all think of us as Americanos, not United Statians, or whatever).
So linguistically and geographically I think it's a fallacy that we shouldn't call ourselves "Americans."
Update: I corrected a sentence above that sounded kind of funny. I made it seem like no one in the world refers to us as Americans, when I meant the opposite. I think I was just in a hurry to finish for some reason. Sorry.