There are poor men, black men, gay men, feminine men, transmen, and all kinds of men who do not control society. Priviledge isn't really black and white, especially across the gender binary.
As a woman, I think blaming all men doesn't seem very productive to me personally and I think working together to create a fair society for all of them.
This is particularly article is a commentary on how the queer community treats bi women like we're less queer because we are attracted to men and that trend of one of many that fuels this pointless narrative that doesn't do much for anyone.
I think anything bordering into essentialism is just a waste of time and fails to show the nuance and complications in the world.
Your point that men should fix it I agree with, and some are. But rather than yelling about the men who aren't fixing it, I'd rather celebrate the men and women who are fixing it.
Also feminists have fought for certain men's right as well as women's rights before, like in Canada we've fought for gay men to donate blood. It's not new to want men's and women's lives to be better as a feminist when certain structures make it harder for them