That person is not a progressive, just a brainwashed idiot.

If you go look deep into feminism nowadays, it's full of ignorant people, even men, that not only say (indirectly) that women should be MORE than men, but also thinks ANYTHING that seems to exclude women in any shape or form, like "man-at-arms", is some kind of terrible crime.

I applaud the joke "go back to the kitchen" in this situation, because ridiculousness should be met with ridicule.
I also defend what "feminism" should stand for, gender equality, not forgetting that men and women are a little different by nature, so it's more about equal opportunities.