"Reverse discrimination" IS a fallacy.  It doesn't exist and presupposes only one type of discrimination.  Only discrimination exists, either positive or negative.  When you only hire a man, you positively discriminate for men, and against women.  When you only hire a woman it's the opposite.  It's just good old discrimination, plain and simple, with some people believing it's justifiable, and others no.  Discrimination has always been justified by its supporters, in whatever context.     

On a personal note, I find the whole use of the word "privilege" misguided.  Like many others, I was taught that privilege is earned.  While I fully understand the argument that some people are born with more advantage than others, I find that the use of the word "privilege" weakens the argument and preaches to the converted.