However, there is an assumption that women aren't interested in, and/or aren't good at, many jobs that are currently held by a male majority. This is an institutional problem. It starts at childhood social indoctrination times in grade school. Parents do it to their own children and schools reinforce it. That's why we end up with "few women engineers".
If we believe, as a society, that this is a problem, then we should address the root cause and let everything evolve naturally from there over time. Attempting radical and sudden social change by starting at the top, and placing less qualified, less experienced women in positions of leadership, is the exact opposite way society should seek to solve it. It does nothing but breed resentment, and the belief that women are incapable of reaching these positions without special treatment. Not to mention our businesses will suffer in the meantime because less qualified candidates are being chosen for positions.
There should be equal opportunity, not equal outcomes. Mandating equal outcomes is oppressive, unfair, and just plain stupid. Nobody is saying women can't go to school and study in certain fields, or get low level jobs at certain businesses. What we're saying here is that women should have to work their way up from the bottom just as men do, so that only the best achieve the highest positions, based on their education, experience, and talent. If women have equal opportunities, but choose to have different priorities and thus end up with different outcomes, that is not something we should condemn.
No, because there are undeniable biological differences between the sexes that are far deeper than, say, skin color. Men are "underrepresented" in professions such as nursing and teaching. Actually, in some of the most "equal" societies, such as Scandinavia, the gender disparities between historically "female" professions (such as child care or nursing) and "male" professions (such as physical labor) are even greater than in relatively less "equal" societies such as the US and Canada.
There's actually quite a bit of overt discrimination in teaching at the elementary and pre-K school level. Men are strongly discouraged from taking the requisite classes in college and are rarely hired for actual positions. Any man who expresses an interest in teaching kids younger than middle school age is regarded with suspicion at an institutional level. Rules are designed to discriminate against men, with the assumption that any man who chooses a job in early education is gay and/or a pedophile. Fathers are largely kept away from even volunteering at schools. Many (mostly female) administrators at this level hire no men at all. At the pre-K level in particular, only 3% of educators are male.
This state of affairs came about as a result of the feminist movement wanting to take over early education and thus shape society starting with young kids. They saw education, particularly early education, as supporting a white, paternal society, and sought to take it over. They wanted to feminize early education and eliminate male influence, in order to re-engineer society. The result is the above. Now, children are isolated from men most of the time, fathers are treated as second-class parents, and boys are labeled with learning disabilities 3 times as often as girls.
If you want an example of how affirmative action seeks to create "equality", early education is a prime example.