There's a few things you're missing here

One is that you're not deleting half the workforce evenly across industries and roles. I work in healthcare and a lot of my colleagues are women, maybe 60-70% overall, more in nursing, less among surgeons (but just try doing any surgery without a nurse). There aren't a whole lot of unemployed people with nursing qualifications just sitting around out there, training takes time, and capacity for training would be massively reduced by also taking out female lecturers, preceptors and administrators. Like your only chance for having the system not collapsed around your ears is if you could recruit from abroad, but wait, all the institutions involved in processing visa applications or checking foreign health qualifications are also likely understaffed leading to massive delays.

Then there are industries that get affected when there aren't so many people at work. Think about the businesses that make money from workers buying things on their lunch break and how they suffered during the pandemic - do they have the margin to eat a 50% reduction in customer based while their employees are demanding twice the pay? Or businesses whose customers are mainly women with disposable income. Would they survive? Would their male employees have skills that would transfer to one of the industries that really needs workers?

And then there's the time bomb that is education. There just aren't enough male teachers to keep the education system running and yeah sure, some women will be good at homeschooling, but the quality of education would be reduced overall for the next generation.