If you don't mind, I'm going to knock down your claim of satire.

Ironic/satirical sexism involves making derogatory misogynistic comments in an attempt to seem witty and above it all. Specifically, the idea is to sound ironic, as in “I’m allowed to say this because of course I’m not sexist, so it’s funny.” It’s an aspect of a larger part of culture which wants to seem jaded and urbane and oh-so-witty. Using language which is viewed as inflammatory or not appropriate is supposed to push the boundaries and make someone look edgy, but it only really comes across that way to people who buy into that system. To everyone else, it’s just misogyny.

The thing about using sexist content in an “ironic” context is that it still perpetuates sexist ideas, and it is, in fact, sexist. While people may ardently claim that they are not sexist, the people who engage in ironic sexism are overwhelmingly male, and they clearly have some unaddressed issues which are being subverted in their attempts to be edgy. Sometimes, they are actually explicitly misogynists, and they are using ironic sexism as a way of presenting their sexism in a way which will be acceptable within their social groups.

Ironic misogyny often hides under the unassailable guise of satire. People who suggest that something is misogynist, and not actually funny, are told that they obviously just don’t get it, and that the whole point of humour is to push boundaries. They are told that the misogyny is so obvious and overstated that it’s meant to be laughed at, and that people are laughing at the misogyny and the misogynists, not supporting the ideas which are supposedly being mocked. But, oddly enough, a lot of misogynist satire doesn’t read that way, and it ends up just being misogynist, full stop. (Let's point out here that the quintessential satire, A Modest Proposal is funny because it's so absurd. Kitchen jokes aren't all that absurd; a large number of people still actually believe this.)

The other favorite defense is, of course, to claim that people are being “too politically correct” or “too sensitive.” This is supposed to be a pithy insult which indicates that the person pointing out offensive behavior is too uptight, but in fact, it’s just silencing. Saying that women deserve to be treated like human beings and that discourse should be respectful has nothing to do with being too sensitive, and everything to do with genuinely believing that people should be treated equally.