This metaphor isn't very good and is bound to get confused, but it's the best I've been able to come up with.
"Privilege" is like a window. It protects you from the harshness outside, but its glass also distorts your view. There are lots of different kinds of privilege - being male, being white, being rich, being healthy, being smart - and they stack up. Each one gives you a little more protection from the world, and each one distorts your view a little more. But from inside, you can't see the window, and you get so used to the distorted view that you don't realise it's there most of the time.
(I don't like the word "privilege" for this next bit because it's loaded with other connotations than the point I'm trying to make. It's a privilege when it affects your thinking, but in terms of how they affect your day-to-day activity they're more like advantages - stuff that makes it easier to overcome different challenges.)
There's an assumption however that because you have more advantages than someone else, that automatically means you can't suffer any hardship - and moreover, you're not in a position to have an opinion on the hardships suffered by others. You can't understand it, and you certainly can't talk about it.
This is, in my experience, usually delivered in an aggressive, dismissive or condescending way; a rock thrown at the window. I know, logically, that the rock was thrown at the window of my privilege, to remind me that the window's there. But from where I was standing at that moment, it looked an awful lot like it was being aimed at me.
My point, in the argument that started this train of thought, was that the root of a person's misogyny (even though it's ultimately unjustified because of the privilege they stand behind) isn't going to go away if it's only met with that hostility. To that person, their insecurities are real and valid and frightening, and being dismissed as oversensitive because they haven't had it as hard as someone else is only going to make them feel more threatened - which isn't going to defuse the situation. It's going to make them more angry, feel more threatened - it's going to validate their fears.
Snark might win the battle, by shutting out sexists and misogynists1 in the short term. But it's not going to win the war because that exclusion, real or imagined, is what's driving them in the first place.
1 And me, as it turns out. I thought, as I said yesterday, that I was being reasonable - I was trying to be, at least. But I'm tired of this argument, so I'm going to leave it to the extremists on both sides.