Definition.com
Nigger is exclusively a word for black people for the same reason that fat people get to make fun of skinny people, and poor people get to make fun of rich people, but not the other way around... namely, sometimes the people with the most shit have to shut up and let other people talk shit.
Definition.com
Nigger is used amongst black people themselves because they share in the same oppressive situation, the same collective condition known as nigger, so while we shouldn't say that white people can't say the word, it's that, given the history, they shouldn't want to.
Definition.com
Nigger is only able to be used by black people in the same way that only football players are allowed to pat each other on the butt when they're on the field