When there's equality of opportunity, then women tend to outscore men on average in Danish high schools (and this trend is true all over the world, given any equal-opportunity situation).
Since women are scoring higher, they have more choice in what fields they want to study since the grade average tend to determine this. In contrast, men have to pick the subjects they can "get" which tend to be the STEM fields. All the typical "female subjects" are the ones which usually requires unethically high grades in Denmark.
Now, to convince a young woman to study STEM not only requires you to convince her that it is an awesome field (which it is, and we should definitely encourage that!). It also requires you to argue why she shouldn't put all her high-grade-work into effect by gravitating to a subject which is women-dominated and the competition is fierce. And that she can live out her dream: she has worked hard and can be anything she wants!
Whereas the young boy who were lazy in school (because he had a hobby of playing a lot of computer games) has to pick one of the "boring fields" where they accept anyone because there are always space for more people.
It is a two-sided situation and as much as you want to focus on the women not picking a given area, you have to focus on why men are so friggin' outright obsessed with the same thing.
There is one type of study which determines part of this: namely that men are interested in things and women in people (on average: The split is something like 33/66 and there is a considerable overlap - but it is one of the strongest gender effects!).
Of course, reality is a mix between biology and environment. And thus also location: the strong welfare state of Denmark could easily play a role.
I think realizing this is a false paradigm will be the next phase in the evolution of this social issue, I just have no idea how it will happen or how it will play out.
https://www.youtube.com/watch?v=VrOp8ewzJDc
So a hiring rate of 40% would indicate a level playing field in hiring. 33/40 is around 82%. The doubling down policies of "The (metaphoric) beatings will continue until equality is achieved," would seem to be misplaced at the workplace level. If there is systemic bias, it would seem to exist at the educational level.
https://www.huffingtonpost.com/belinda-parmar/sugar-and-spic...
The general conclusion being that men tend to focus on ideas and woman gravitate towards people.