The 'African' in African-American acknowledges the connection to a number of African cultures, not one in particular. The 'American' shows the nationality and culture of the United States. A person born in Nigeria is still Nigerian even if he or she comes to the United States and lives here for the rest of their life. If that person wants to say that they are an American citizen, they would simply say "I am an American citizen". His American-born children could correctly call themselves Nigerian-American OR African-American.