I agree with equality of opportunity over equality of outcome. That leaves room for there to sometimes be times we'd actively encourage certain groups to explore certain things (eg like a PP said, female only woodworking or something) as these can give the opportunity for that group to do something they might not usually. Having a woodworking group that MUST be 50/50 men and women is an entirely different thing.
Positive discrimination has negative side effects that people often don't discuss. Eg. If you say 50% of leadership positions must be held by women, then a lot of people are going to suspect that at least some of the women in those positions are there due to their sex as opposed to their ability. It undermines the whole enterprise and casts a level of 'suspicion', for want of a better word, over the abilities of ALL the women in those positions.
Far better to think creatively about things that can be done to encourage women who could, but don't, go for leadership positions. For example, a lot of women don't want to throw themselves into their career because they want to be around more for their children. And not just because Patriachy but because Motherhood - plenty of women want to be highly involved in the day to day of their kids lives. But top leadership positions often aren't conducive to this - I've actively avoided promotion at work for this very reason. If there were things in place that meant I could move forward at work (next step would actually be a leadership position for me) without fear of the expectation the role should take over my life, I might do it. I don't know what could be put in place really given the necessary extra work responsibilities a leadership position entails, but that would be far more effective at encouraging women rather than insisting it must be a 50% split with no structural changes to enable it. FYI I think that this is what James Damore was getting at in his infamous memo - what can we change to make tech a more desirable field for women.
Quotas for 50/50 are IMO quite a 'patriarchal' way of dealing with the problem. Inflexible. Assuming that women should just 'act more like men', with no consideration to the average differences between men and women in terms of priorities, does no favours for women.
I don't understand this pretence that all women do more with kids and at home because of horrible men and the Patriachy, that they're all itching to get out there and be CEOs but for society and their annoying children. This simply isn't the case for a lot of women (it is for some of course). We need instead a shift for all roles in society from caregiving to leadership to be valued so men AND women can do what they want without pressure or shame. Quotas just reinforces the believe that caregiving/raising children etc is fundamentally 'less than' corporate and career success. We're always going to need to have both though.
JP also isn't wrong that in the most egalitarian societies, with high support in terms of parental leave, affordable childcare, equal taxation policies etc, the split of how many men and women are in certain roles only deepens, suggesting there must be something else at play. The most 'equal' societies in terms of jobs are often developing countries where everyone has to work backbreaking farm labour/mining etc. Basically places where there is less choice.