Put simply, men are not systemically oppressed. Whilst it's true that most male individuals are oppressed as members of the working class, and might also be oppressed as people of colour, members of sexual minorities, migrants, trans people, disabled people, etc., men as a group are not systemically oppressed.
Women might make assumptions about them or be unduly suspicious of them because of their gender, but this is not systemic oppression and is largely a result of women's oppression. Men might be expected to be promiscuous, dominant, emotionless, physically powerful, but this is a direct cause of women's oppression and oppresses women more than it does men. Men who are seen as "feminine" might be shamed, but this is because femininity is seen as inferior and is therefore even more inseparable from women's oppression.
Now let's look directly at the so-called men's rights movement's flagship issue: the family courts. They cite the alleged bias of child custody cases against the father as an example of "female privilege". I don't have the time to go searching through media reports and statistics which themselves are skewed as often as not and try to sort the fact from the fiction, so I don't know if such a bias actually exists or to what extent... but that isn't the point. If such a bias exists, then in the big picture it's a rational bias in our existing society in which men are all-powerful in sexual and relationship politics. It's taken for granted that men are the active, and usually dominant, partners in any heterosexual relationship... so much so that a lot of heterosexuals see the more active partner in a lesbian relationship as "the man"; this assumption is rarely challenged, and any time the reality deviates from it, society does its best to make it into a badge of shame for both parties. Any woman, particularly a heterosexual woman, who takes charge of her own sexuality is shamed as either a "slut" or a "prude" - often both, as paradoxical as that is. And the contrast between young girls being largely discouraged from any strenuous physical activity and young boys being constantly bombarded with the "need" to be good at running, good at sports, strong in the arm, above all good at fighting, means that the natural physical advantages of most men over most women are even more pronounced. In this context, it's scandalously easy for a man to be both an abusive partner and an abusive parent, and certainly far easier than for a woman. So to campaign for family courts to be "less biased" to women without offering a better solution, whether any individual campaigner is aware of it or not (and I don't doubt that many "men's rights activists" genuinely believe that men are persecuted and are blissfully unaware of their complicity in women's oppression) is to campaign for the last legal recourse of heterosexual women in abusive relationships to be undermined. Any honest campaigner for an equitable family court system should be first and foremost a campaigner for women's liberation.
Every way in which men are "oppressed as men" is inseparable from women's oppression, and can only be solved or mitigated either through women's liberation or by oppressing women further. So every "men's rights activist" who is genuinely not misogynistic should be primarily a women's rights activist. Unfortunately, the "men's rights movement" as a campaigning community almost never mentions women's rights except as a token or in an attack.