This is complicated, so my comment will be long..

When the first lists of male privilege and white privilege came out I thought the device was a great tool for introspection, for seeing how different life is for people who are not your sex and/or your race and so on. I saw that as something which would increase understanding and compassion, and contemplating one's privilege looked like a great idea.

But then things changed, and I started seeing the concept used in a different way: To shut people up in conversation, for instance.

That wasn't a good development (because if you take the concept to its very extreme interpretation, everyone else except the most oppressed person on this earth has privilege, and even that most oppressed person might have privilege over all dead people, though we obviously can't tell), but a different development was even worse:

If some people are privileged and others are under-privileged, then NOBODY is currently being treated just right! We no longer even know what fair treatment is!

This is a BIG difference to the older way of thinking about these issues where some groups were seen as under-privileged and the job was to improve their lives until they were treated the same as everyone else.

But if everyone else is now seen as privileged, then we cannot pull others to that level, because then we would all be privileged, and that is impossible. So the obvious consequence of the widespread use of the privilege concept is that for justice to occur it centers the idea that lots of people must be made worse off.

That could be factual (or perhaps not), but it's not the best way to sell being an 'ally' to others, because it centers the losses that will happen to you and yours if you are currently seen as privileged.

I understand the satisfaction that turning the tables this way causes, of course, because it makes, say, the problems of misogyny and sexism something men should largely solve and because it forces the more dominant groups (men everywhere, whites in many countries and so on) to actually think about the ways their lives are made easier by that unearned perk of a group membership. But psychologically the concept is like using vinegar to attract flies.

Another problem with the way the concept is being used has to do with its use in, say, "cis" (sic) privilege:

One axis of privilege is chosen over all the others, and if we are not really careful we start forgetting about the other axes. To give you an example, someone believing in 'cis' privilege might then have to argue that a rich man in Saudi Arabia who truly wants to live as a woman but is not allowed to do so there is less privileged than all the Saudi women who are under lifelong male guardianship and have very limited rights. People who use the privilege terminology seldom use it carefully and seldom note that there are many different privilege axes (if we go with that concept) and that when we compare two people's overall relative privilege we must take all those axes into account. So even if one believed in the label 'cis', cisgender men and cisgender women are not equally privileged, and because of that men who transition may not, in fact, be less privileged, overall, than women who never transition. But that is what is usually argued.