Old fashioned chauvinists don't necessarily hate women. They are the beneficiaries of a world view that holds women to be inferior, and they don't like being reminded of the fact, but they aren't necessarily motivated by personal dislike of women: they just favour the status quo because it benefits them.
Woke bros, on the other hand, are fully aware of patriarchy and, on paper, opposed to it. But they don't really want to overturn it because, just like the old-fashioned chauvinists, they benefit from it. Dilemma. This means they have to find a whole other raft of excuses not to listen to women. In the good ole days pre-about 2005, this was a bit tricky - they had to rely on telling women that their rights were important, but not as important as black/gay/working-class people - we were going to get their full support just as soon as those priority issues were sorted. But then, What light on yonder window breaks? It is transgenderism, come to save woke men from the risk of one day having to centre women. Now they can support women: just the ones with penises, not those pesky ones with vaginas. Problem solved.
Completely this.