The term African American was coined by Blacks in the United States, meaning those whose African ancestors were brought here in chains. The term was coined by those who were once called Colored, Negro, Afro American, Black American, etc. etc. I think that most people know, particularly those whose families have been in the U.S. for generations, that African Americans are the descendants of the Africans brought here during the Slave Trade.
Now that we have other Black people in the U.S. who are from various different parts of the world (Africans, Jamaicans, Haitians, etc.etc.), people want to act like they don't know who the term African American is meant for. Is it okay for someone who was born in the United States but has African parents to call themselves an African American? I say sure if they want to, but when I personally think of African Americans I think of people like me, whose African ancestors were enslaved in the United States. I personally LOVE the term African American because I think it sums up what I am quite nicely. I'm an American because I was born here and many generations of my family were born here but I am proud of my African heritage also. I also know in doing my own genetic research that DNA doesn't change just because you are generations removed from your ancestors. The DNA my ancestors had is the DNA that I have, therefore I am also African. You'll find this for yourself if you do your own genetic research on DNA, mitochondrial DNA in particular. A good place to start might be
www.africanancestry.com. My DNA has been tested and it matches that of three tribes/countries in Africa.
It's all about how you define yourself; other people will define you however they see fit. My husband is from Ghana, West Africa and he does not refer to Whites as Africans, even if they were born in Africa, even if their family has been in Africa for generations. To him, they are Europeans or Whites in Africa. He has also been living in the United States for quite a while but if you ask him he will very proudly tell you that he is an African...living in America. He does not consider himself or anyone like him to be African American. He also has no problem in being called Black; he considers all people of African descent to be Black. Ethiopia, the birthplace of modern man, translates into "Land of the Blacks."
The bottom line is call yourself whatever you feel comfortable with and if someone calls you something you don't like, kindly correct them. That is all that you can do. I'm African and I'm American so African American suits me just fine.