I have no problem USING the term, but I've always had a problem understanding "African American."
In general, I know it refers to a American cultural/racial group descended from West African slaves.
I remember times Pres Obama had to do little linguistic hurdles to avoid to strongly identifying as a member of that group, since his own (black) history is actually from Africa, not a member of the group commonly called African Americans.
That group also does not include the millions from the African continent of the "Arab" ethnic group, nor white people descended from colonists, who come to America.
I tend to use the term 'black,' and no one black has ever told me they prefer otherwise.
Oddly, when I use "African American" I've been corrected several times, including, "No, I'm Aboriginal" "No I'm Haitian" and "I'm Canadian."
Not an ideal term, but whatcha gonna do?