She's saying this because she's right. Women writers on Climate Change and Global Warming are often treated dismissively here on Medium and in general.

As for "de-legitimization", it's OK when they do it to her, but not if she does it to them?

These bastards, and I use that term because a lot of them are shills for the fossil fuel industry, need to be de-legitimized and villainized. They are engaging in a disinformation campaign and part of their methodology is to de-legitimize women's voices in the Climate Change movement.

They want it to be unfriendly to women.

Here's something you can do to test the "female author effect". Try opening a Medium account using a female identity and write on Climate issues for awhile. Then we can talk.