Presumably you're referring to the origin of all human life
Uh, no, actually. If I was doing that, then, seeing as we all evolved from very small reptiles living in the stagnant swamps of Pangea, I'd be calling EVERYONE "Pangean Americans".
See, there's this thing called vernacular language. That is to say, the words and phrases "we"- the common man- use in every day speech, whose meaning may or may not conform directly to potential logical, or, in this case, technical/specialized meanings of the words. Yes, yes, splitting hairs about "Africans". Very cute. I'm surprised you're not trying to be difficult about the word "American", either (but but but, why are only people from the US Americans? Aren't Mexicans and Canadians American, too? *feigned puzzlement*)
But since you asked, I'll answer. How far back in time is it acceptable to go? However long it takes to identify the first common non-New World ancestor of the person in question, or perhaps, the first DOMINANT ancestor with whom the person in question would identify or be identified with (by the "average person") culturally and ethnically. This naming scheme isn't limited to Africans-Americans, either; it's a common feature across all groups within the English language. We identify people as belonging to other groups, such as "Italian-Americans", "Arab-Americans", "Native-Americans" (who, again splitting semantic hairs, aren't actually "native" to the continent at all, but are rather descendents of a number of waves of Asiatic immigrant groups). This is why, for example, my friend Ryan strongly identifies as an Irish-American, despite his family having lived here in the States for four generations. If you can't understand this and think it's silly or wrong, well, I guess that's your prerogative. By all means, next Saint Patrick's Day, go out and tell everyone you meet why you think folks shouldn't be called Irish-Americans.
Another thing you've got to understand is the
sociological aspect of African-American-ness. The term "African-American" is often viewed as a "politically correct" one; that is to say, a descriptive phrase specifically condoned by the progressive sociopolitical establishment. This may sound like a pejorative analysis, but it's also quite accurate. "African-American" gained currency as the preferred term to be used when speaking about "blacks" back in the 60s and 70s because it was the term preferred by radical black academics and community leaders. Can't really blame them, since at that time, most people called blacks "coloreds", coons", and "a word my mother wouldn't appreciate me saying, likely"! "African" was a key word- many of these blacks sought to reclaim "their" heritage, their authentic, pre-colonial heritage, one not marred by centuries of slavery and white cultural imperialism. You could argue that "African-Americans" really have little in common with true Africans, and aside from genetics/skin-tone, are more European than African. Nevertheless, in the wake of the civil rights era, it became extremely important for black intellectuals to emphasize their African origins, and to encourage their less-well read brothers to do the same.
In other words, if you've got a problem with African-Americans being called African-Americans, you should probably go take it up with them.
Here's some contact info for the King of Black People. I'm sure he'd love to hear your thoughts on the matter!