Both men and women suffer from gender-based social expectations that are to some extent not fulfillable and likely interdependant. But there is a difference.
I’m a bit neglectant to speak of „suppression“ in regards to men, since men are not as much „suppressed“ as we are „uppressed“. This means: Social expectations for men usually aim at independance, activity and control. Being able to repair stuff, being promiscuous, physical strength, etc.
Of course, many men fail at this. In a way, all men do. Not everybody can or wants to live up to these expectations, despite them being inconsistent or even contradictory. As a consequence, many men feel inadequate for all of their lives, damage themselves or others – or exert power over people over which any man in a patriarchical society can exert power over, no matter how small and „unmanly“ one is: His wife or women in general.
The social expectations towards women on the other side are coined by passivity, abstinence and privacy. We are not always aware of these expectations, but the consequent submission is certainly demanded from women in society, as shown in some of the research above or anywhere in comment sections in social media.
250 years of enlightment and feminism on (if you think enlightenment without women fighting for women would have led to the relative emancipation we enjoy today, re-read Kant), women are still expected to be passive, private and subordinate creatures, who need to adjust to men in public spaces. As also shown in the research above, women are apparently regarded to be less worthy, less able or generally less competent in at least most fields of modern work. This is something all venerated modern sociologists agree upon (check out Judith Butler, Pierre Bourdieau or, if very understandably you find these authors too complex in their writings styles and you happen to understand German, Albert Scherr).
If from any of this you draw the conclusion that somebody would be waging a war against men, you are thinking in the lines of people you probably call „feminazis“, yet I refer to as „terfs“ (Trans-Exclusive Radical Feminists): These debates aren’t about putting men and women on two sides and comparing who is somewhat „better“ or more of a victim. These debates are about the good of us all. We are all at the same time perpetrators and victims of gender expectations – all in different ways.
In general, however, and this is perhaps the actual problem, we have this situation: The gender expecations applied to boys as opposed to the ones applied to girls result in a reality, in which almost all positions of power are occupied by men. This is true for traditional families, for companies, armies, nation states, and so on. And this is a big issue, because:
A) it makes it harder for people not belonging to this group to participate in this kind of power for several reasons, such as the expectations being re-affirmed and/or people belonging to the group in charge feeling threatened by „outsiders“ closing up to them, and
B) homogenous leadership hardly makes decisions for heterogenous populations (unless forced) and/or isn’t aware of detrimental effects their decisions have on people who are not part of the group that is in charge. A committee consisting only out of men is very likely blind to the way their specific subject of interest looks from the perspective of a woman, just like most men are blind to and often surprised by how omnipresent fear of sexual violence or stories of weird strangers following them through the streets are in the world of many young girls.
Now, this being a social problem and humans not being able to exist outside of society, this isn’t a problem for individuals to solve, but for societies. States, in fact.
But wait, you might say now, isn’t everybody responsible for their own good? Don’t we live in a world in which it has been proven again and again that even the most belittled person could dig him- or herself out of the ghetto and become boxing-legend Muhammad Ali?