I agree that Weaker Sex was more focused on the male perspective, but I get the impression that the original idea teased in that article may have been a little too much on the female side. To capture both perspectives and draw in viewers, I would try looking at a more common ground. What do men and women argue about? Give something both can relate to so that viewers are engaged; and then take the opportunity to maybe get them to see things from a different perspective.
One example would be from an article I read years ago - the argument over what to eat. The woman usually asks the man, and then the man often says it doesn’t matter to him and defers to the woman to try to please her. This instead has the opposite effect and angers the woman. And if the man does present a decision, the woman starts giving other options which angers the man because he thought the problem was solved but she wouldn’t seem to accept it.
Why does this happen? The article presented that what the woman is looking for is options to choose from - not to be told what to do or have it thrown back to her to decide alone, but instead be given options she can pick from.
So how do you use this to present a different way of looking at things through an alternate reality where women dominate? Maybe you could have a world where everything is polled. Arturo goes to buy an ice cream; he makes his decision; but the clerk presents three other options before allowing him to buy. This starts to annoy Arturo who demands his ice cream; and then the clerk says he needs to fill out a satisfaction survey. Arturo loses his cool.
The theme would be “How Arturo learned to love and loathe the poll”. Keeping the election plot line, we could see that primaries aren’t used on this world - for instance, you could have 3 Democrats to choose from on general Election Day. Arturo would be the unusual sole candidate for his party; polls showing that people like his solitary strength as one, clear choice that cuts through what many voters have come to see as a muddy process of uncertainty. This then leads to the crying stunt to throw the election and shatter what people perceived Arturo to be. Arturo would no longer be an easy, quantifiable certainty.
It’s not much different than what we got, but it opens a door for discussion of why primaries are not used on this world. Then we can explore what women want and how Arturo’s decision to cry ultimately didn’t give him what he wanted (losing the election). Why? Because after the crying, women were given their multiple options to choose from in one man - the ability to choose drew them in where they were previously repulsed by his one dimension.
Anyway, one rough idea of how the differing viewpoints could be presented. There’s a lot to mine there in the differences between how men and women think; and better avenues than just plugging a woman into the bully mentality or sexual predator stereotype.