Too often there is this separation we invent where misogyny is a ubiquitous tool of patriarchy while misandry is somehow separate. This becomes so intense that many are not even able to admit that misandry is even theoretically possible, and even if it's undeniable it is still seen as highly irrelevant to patriarchy.
But misandry does advance patriarchy and it is a force that intensifies misogyny.
Consider homophobia. This is an obvious case where misandry advances heretopatriarchy. Certain men can entrench their status through an infrastructure of hatred against homosexual men that can be accessed by nearly everyone else as well.
Consider transphobia. Another obvious realm where misandry is at play. Trans men are shown hatred in ways that are unique to the experience of cis men, and these experiences drive cis heteronormativity.
Consider how our actions and ideas impact the world. If we live in denial of misandry we live in denial of patriarchy. Denying misandry does not make you a quality feminist. It does not make you theoretically sound. Hating men just gets in the way of challenging patriarchy.
Consider how misandry enforces gender roles. Misandrous discourse functions to discipline people. When misandry is denied, there is almost always an element of "you have to man up, because women are weak." The narrative is familiar; women are subjected to patriarchal violence and are thus too hysterical to have sound or reasonable options about men, thus, men must internalize misandrous attitudes out of sheer emotional intelligence and masculine willpower. The men who fail to do this are weak, unable to maintain a rational, stoic attitude and are thus lesser, unmasculine men. Men who can master their performance of masculinity in a self-denying or sacrificial way will benefits from misandry but will certainly be thoroughly disciplined by it.
Women, other non men genders,and queer communities often play a role in policing masculinity for patriarchy which may obfuscate the patriarchal power at play. This ultimately reinforces misogyny by haphazardly enforcing binaries, devaluing feminity, and promoting a supremacist view of masculinity.
Let me paint a situation. Imagine a comedian making a joke about their trans wife; that she removed the worst part of her--being a man. Everyone laughs in support of trans women and implicitly they laugh AT trans men and cis men. Next joke is about how stupid bisexual women are for dating men, how they make the queer community worse.
Now imagine you are a man who wants a little clarity in life. How should you feel about such language which is clearly both misandrous and misogynistic? How should you feel that it is directed at you, as a man? I'll tell you:
You should feel safe because you are a man. If you don't feel safe it's because you are a weak man, incapable of performing.
You are getting very mixed reactions to this post because you are using incorrect terminology, and misunderstanding some things, but also are seeing some real problems. Patriarchy does hurt men too. As all oppression hurts the opressor. But that is not because of "misandry".
Misandry is hatred of men. Because they are men.
If you hate a gay man for being gay that is homophobia not misandry. If you hate a trans man for being trans that is transphobia not misandry. If you hate a black man for being black that is racism not misandry.
You are taking misandry to mean any prejudice against a man. That is not what it is. Just like if you hate a lesbian for being gay its homophobia not misogyny. etc.
A man will never experience actual systemic hardship simply due to being a man under a patriarchal system. Men can experience systemic hardship for OTHER reasons though. That is not misandry.
The strict gender binary, and pressure for men to be masculine and women to be feminine is also not misandry. The term for that is heteronormativity.
This is why you get so much push back. You are having a communication problem.
What you should be focusing on is how the act of oppression itself harms everyone. I think that is what youre trying to get at. If you can refine your language, and viewpoint a bit i believe you will have a much more positive reaction to the points you are trying to make.
For example. A white person in a racist society. They may not be able to love people of another race openly, or have friends of another race, or act in certain ways that are deemed 'non-white', or various other things.
None of these are anti white racism. They are restrictions placed on the oppressing group by themselves in order to maintain the otherization of the oppressed group.
Intersectionality can make understanding things like this in the real world a bit confusing sometimes. So while this might seem obvious to you in this context that may be why you feel differently about this same phenomena as it relates to partiarchy.
I hope that explained it well enough.