False Justification and/or Logical Fallacy

I have a friend who is using the existence of a double standard to justify behavior.

his argument is this: Because black people can use the n word, anyone should be able to use the n word. Or at least, black people can’t complain when other people use the n word.

It stands to reason that just because group A isn’t following the rule, that’s not justification for group B to ignore it.

If neither blacks nor whites should use the ‘n’ word; if blacks use it then whites can use it. That seems like a fallacy. But which one?

The big problem is your friend assumes all rules are the same for everyone. This is a false assumption. For example, a doctor can give medical advice; a life coach can't (unless the life coach is a medical doctor). I can smack my wife on the butt; you can't. Etc. It is the misuse of the double standard .  
Instead of judging two situations by different standards when, in fact, you should be using the same standard, your friend is judging two situations by the same standard when, in fact, they should be using the two different standards.

As always, check your premises: The claim “Because black people can use the n word, ...” may not be true. Puff, there goes the discussion.

I suppose it could be tu quoque because the argument states that a particular position is false or wrong and/or should be disregarded because its proponent fails to act consistently per that position. 

Or, perhaps, Fallacy of Composition because it assumes that something true of part of a whole (some black people use the “n” word) must also be true of the whole (all black people use the “n” word).

Or, stretch a bit and get the If-by-Whiskey fallacy. At least, it is more fun.

P1: A is allowed to do blabla.
P2: Letting A but not everyone else to do blabla is practicing double standard.
P3: Practicing double standard is wrong.
C: Therefore, if A is allowed to do blabla, everyone else should be allowed to do blabla.

Most likely P2 is to be challenged. 
For, black people calling themselves the n word but not letting non-black people to use the word is not practicing double standard. The n word, when used by black people, is self-referential; the n word, when used by non-black people, is not self-referential. 
I can self-reference "this silly" in my email to a close friend.
Is it appropriate for a stranger to use "you silly" to refer to me?
A friend of mine may use "you silly" to refer to me because the close relationship has altered the pragmatic part of the phrase, not because I and my friend are practicing any double standard.

Further, P2 does not have to be in any language usage setting. There are a lot of settings, including the ones mentioned in the posts above, in which A's doing blabla but not others' doing blabla is justified. By the way, a man may not be justified to smack his wife on the butt. In fact, a man, most likely silly, rude, and violent,  who smacks his wife on the butt, is almost always not justified.  

To conclude, if A is justified to do blabla, but others are not justified to do blabla, then letting A but not others to do blabla is not practicing double standard.

I don't really see any type of fallacy. It just looks like a bad argument that has one fatally false premise. If I were you, by the way, I would not become a man who smacks his wife on the butt, or I would not become such a man's wife.