While I agree with you that the teacher in this post is wrong about what this is, I don't think labeling "gender bigotry" indiscriminately as something both sexes do under one umbrella is accomplishing anything but minimizing the struggle women have endured for basically all of human existence up until the last few decades.
Personally, I wouldn't fault this woman for thinking what she does if she's willing to accept a broader explanation later, given that women have literally been sold as property up until a couple hundred years ago.
Women have the right to at least posit the ways they as a group have been held down, and that includes accepting their indignation and allowing them grace for when they're wrong, because without those things they won't actually learn the truth.
Further than that, I think it's necessary for women learning now to have the same realization this one did that women throughout all of history save for this recent tiny sliver have been oppressed. Even if it's built on an incidentally faulty premise, that doesn't mean the realization itself is wrong.
Covering up the discourse by labeling the process of realization as "gender bigotry" is itself an attempt at erasure, and very much puts you on the side of the oppressors, just because you think it's distasteful to have this realization yourself.
I'm sure gender bigotry exists in the direction of women towards men. This ain't it.