Another thought and hypothesis...
Short version: I think we need to raise girls and acculturate them at the youngest ages to understand and be able to operate with men within male spaces.
Long version:
Okay... men and women tend to be different. Not universally, but tendencies as a group. This is not a judgment that one is better. Just different. Apples:Oranges.
In the past, societies divided the world and the tasks that needed to be performed in it along gender lines. Broadly people "knew their place" and were expected to stay within it. I do not think this was better.
Now, more spaces are shared as both/neither male and female, and we allow people to self determine what environment is best for them and what role they will play within it.
Boys are overwhelmingly brought up in their most formative years by women in and around female spaces. Infants at home with a mother. (Single mothers and stay-at-home moms are more common than single fathers or stay-at-home dads.) Daycare, kindergarten, and most of gradeschool are almost exclusively taught by women. Usually kids don't get a male teacher until they are far enough along in their schooling where they start to have subject-specialist teachers for things like math and science. That's probably junior high.
Boys have learned to respect and work with women and to adapt their behavior to work within female spaces.
Young girls generally don't have the same experience learning to adapt to male spaces. They just don't get that exposure.
Then you get into adult life and the professional world. Women find it hard to fit into these male spaces. Certain trades like a production, military, or production environment by their nature require a generally "male" mindset. This is a problem. It needs to get fixed. It doesn't matter how you feel about it. A broken motor doesn't care about your feelings.
So, women try to move into male spaces and feel uncomfortable. They've never learned how to adapt to this sort of environment and culture. Some adapt. Some opt out. Some leave offended. Other expect the environment to change for them. This causes friction.
It also causes problems in personal lives dealing with male partners.
Although I can adapt my behavior to fit a female-centric mode, that's not my default or preferred style. It requires effort. The more I am stressed, the less emotional energey I have to spare, the more likely it is to shift to my default operating style. This is going to be offputting to a woman who is not used to adapting how she operates to fit that.
So... what do we do about this?
I think we value the role of fathers raising children. Let them be themselves and go do activities just them and the children.
Take young girls to and get them involved in male-centric spaces. Fix things with them. Play sports. Have them hang out and lend a hand with "the guys".
I don't think this will make women significantly more likely to go into those male-centric fields any more than being raised by women makes men want to become kindergarten teachers. But people will understand and respect the other side better.
I teach social dancing (swing, tango, etc.). Traditionally men lead, and women follow. When I instruct beginners, I do exercises where everyone has to do both roles so they understand and appreciate what their partner is doing. As they progress, I let people self-select which role they want to do for different exercises. The vast majority end up self-selecting the "traditional" role most of the time. But everyone enjoys their role more, appreciates their partners better, and communicates better in a more fulfilling partnership because of that understanding.