It's difficult to reply to that one sentence rant, as you seem to have some mixed up messages yourself. Firstly, I don't know where your comment 'made up claims about gender pay gap' refers to. I simply don't know what your argument is. But, considering women have to take time out to have children, I don't have a problem with them being compensated for that. Women who choose not to have children still have less super at the end of their working lives, so there is a disparity there. Sorting out a solution is the hard part because it means structural and cultural changes in the workplace.
Secondly, 'donning head gear, etc' presumably refers to the 'pussy hats'? Here's a direct link to the FAQs:
https://www.pussyhatproject.com/faq In this context, it is not oppressive. It actually mocks oppression.
Thirdly, 'taking full responsibility for children, etc' presumably means you think women benefit from family breakdowns? Considering the traditional role of women is to take care of the children and men to go out to work, I'm not sure why you would think women aren't taking responsibility for their children. Anyway, mostly both parents work to keep up, and it is often difficult for men to find part time jobs to share child care. That's one area where things could change. For example, a plumber, carpenter, electrician, doctor, or more male dominated professions could make it more flexible for men. This is changing though. Again, 'expecting men to pay for everything' is simply a nonsense. As far as I know, it is very expensive to keep children clothed, fed, and housed, and I'm sure there are not too many women around that can afford the luxury of having a man pay for it all.
Both men and women have affairs too. However, more often than not, its men. If you expect a woman to stay while her husband's infidelity is questionable, then you are not being realistic yourself. It depends on the individuals involved and there are so many variables, as we know from Barnaby's situation.
Finally, the feminist movement is very clear in what it stands for, and that is for women to have the same opportunities as men.
Now all of this is very complicated in practice, so I suggest you go through all of the issues you raised, and try to work out how you would go about it. One way is to recognise the efforts that women make in society to contribute to cohesion and wellbeing. That's what IWD is about. It separates out women's issues so that they can get attention, rather than being taken for granted. It seems to be working, because you have taken time to voice your opinion.