I personally idenfity as feminist. However, I do not and will never support nor advocate that women gain power OVER men. I will and have supported and advocated for women being treated EQUALLY to men; no more, no less. I believe the numbers of feminists like me vastly outweigh the toxic minority that would rather lynch men; we just aren't as vocal as they seem to be, if the OP is any indication. I have participated in two Women's Marches thus far, and in neither of them (for the first of over 1 million participants in my area alone, second somewhere between 500,000-750,000) were there any feminists calling for all men to step down in favor of women or advocating punishment of men for how women have been treated until now. Instead, there were calls for being treated equally, being paid equally, for teaching children from the get go that your gender doesn't matter and shouldn't matter in terms of how you act toward another person in a multitude of settings. That's it.
I don't agree with the premise of the article from the OP. I do not think men should "stand down" in favor of women. I DO think that women should be offered the same opportunities and respect in the same situations, but that's a matter of being treated EQUALLY, not advancing one gender over the other because the other has been in charge for all this time and someone thinks it's time for the first gender to have a turn. This isn't about taking turns, to my way of thinking; this is about being treated the same when I or another woman hold a position of authority to the way a man would be treated, to give a limited example. No more, no less.