I find the term a little confusing, because (for example) if Freddie Mercury were still alive and if he were to move to the US and become a US citizen, I doubt he'd be called 'African American' by anyone, even though he was born and raised in Africa (Zanzibar, to be precise), but he was as white as a sheet, in spite of having Indian parents. Same for Pik Botha and FW de Klerk (South African politicians), and millions of others, yet if they became US citizens, they would in fact be African Americans. So I'm assuming 'African American' = the B word (and I'm not using the B word in case its not politically correct in America, the way it is here. Nobody here would call themselves African British, for example. The B word is the word used by everyone, whether they're B or W)
As for Indians (Calcutta rather than Apache), its the same here, they dont like being referred to as Asians, because Asian generally refers to people from the far east. Also, many native Israelis feel insulted when they're called Asians, even though thats what they are. Same said for people in Cyprus. The people of Malta refer to themselves as European, whereas geographically, Malta is a part of Africa.
As for my friend, I dont think he meant he was insulted by being referred to as African or American as such. I got the impression he was more insulted by the ignorance of the people he was talking to. They didnt seem to understand that people of colour (another term I hate, because we all have a colour) could be referred to as anything other than African American, which I find kind of dumb, because in my own living memory, I can think of lots of terms which have been used. Some respectful, others less so...
And as far as the Italian/Irish/German thing... I also dont understand Italian American (etc). Genetically speaking, its possible to differentiate between an Italian and, for example, a Norwegian. Italian is a defined race, as is Irish / German / Norwegian etc. Yet 'American' isnt a race, its just a nationality made up of many other races.
Anyway, I guess I'll just add this to my 'one more thing that doesnt make any sense to me' list

I'm going back to bed now. I only got up for a pee