I see patriarchal as Biblical and matriarchy as a sign of a messed up culture. God is the Father after whom every every patria in heaven in earth receives its name (Eph. 3:15.) I've got some in-laws married into a patriarchal culture where the woman's family buys the male instead of the other way around. Actually, Anglo culture sort of does the same thing with the bride's father paying for the wedding.
Be that as it may, I do see the higher number of women getting degrees as a concerning trend. Governments pushed having more women go to college. A few decades back, women could get minority scholarships. I have also heard the option that many young men who choose not to persue higher education are making a rational choice considering the low salaries, lack of job opportunities, and student loans. This was commentary I heard during the great recession in the US when a small number of students were protesting about the 1%, and the news selectively covered that as if it were a big deal. There may be some truth to the fact that girls who go to college, at least in the US, tend to major in lower paying fields. Some of the fields of study may be more fields of ideology than true social science. It could be some young men see through the rhetoric. Some politicians treat getting a college degree almost as if it were a religious obligation, like Muslims who make the haj to Mecca, as if one is incomplete without it. It could be some of the young men see through the rhetoric while the girls are more impressionable. So more girls take out $30-$40K in debt to study Women's Studies and get a job in retail afterwards while more boys become plumbers and carpenters.
I have also heard that classrooms are biased toward girls and against boys, and the some of the teachers do not encourage the boys like they used to. I am not sure what the data is to support that.
The point some posters have raised about video games is an interesting one. It could be that too much video gaming has hindered a lot of the boy's minds and motivation by the time they get to college. Atari and Nintendo were popular with Gen-X kids, but a lot of boys in Gen-X went to college.
It could also be the effects of a matriarchical society, where boys masculinity has been portrayed as 'toxic.' Not allowing boys to be dominant in social situations, discouraging leadership over girls, etc. may also have hindered their development. Lack of proper role modeling from fathers in countries where divorce and remarriage or marriage out of wedlock is common might lead to improper development of boys. I'd like to find stats comparing college attendance with these other variables.
Women do like to 'marry up' and men not having the same education may hinder them in that regard.
I also think some of the objectives of government officials are rather foolish. If more men go into stem fields, it may be because men tend to have a wider bell curve when it comes to mathematical ability. Average mathematical ability may be about the same between men and women, but more of the outliers in the 99th percentile tend to be men. More men may want to be engineers. There are very few people who want to work 18 hours a day who are just that driven to succeed. These are the type of people who run things at the top tiers of society. And more of them tend to be women. Most women, and the vast majority of men also, do not want to work like that and have such a work-life imbalance. If women tend to make decisions in favor of work-life balance and having families, and therefore tend to be represented less in the C-suite, governments should not use social engineering to change that. Equality of opportunity and equality of outcome are not the same thing. Jordan Peterson is now a popular speaker on topics of this nature, drawing from the social science research to support his arguments. There are lots of videos of him lecturing on this topic online, or debating and discussing with newspeople or social activists who do not really know what they are talking about on shows he is invited to speak on.