Two things.
I'm not sure where you got that info from, but Arab is language. It is not race. Arabs have been different races. Being Arabic doesn't cancel out one's race. That also explains why people from Iran are not Arab even though they look like their neighbors.
Referring to someone as an Arab has more to do with geography than vocabulary. African isn't a race either, but we all know what it means, right?
I have a good friend with a wife who was born in South Africa. She has blond hair, green eyes, and a milky white complexion. She's an American now. She calls herself an African-American. She truly is one. Ain't it funny?