Misogyny and misandry both exist and are terrible forms of bigotry. But I have my doubts about misogyny being in anyway systemic, systematic or institutionalized like misandrists often claim. It's just their way of downplaying and softening misandry being real and something that's gotten very widespread and socially acceptable and enforced, largely due to it never being given any attention or having action taken against it. You bring up misandry and misandrists will either deny it exists (itself asinine) or claim it's not on a systemic or societal level like misogyny supposedly is. Even though there's zero evidence for misogyny being any of those things. It's just more non-existent opposition they blame their failures and shortcomings on, rather than taking accountability. Hearing about systemic or instituonalized misogyny has quickly become one of the most annoying things to hear them spew.

Not saying misogyny doesn't exist and isn't a terrible form of prejudice (just like misandry), but claiming it's on systemic or instituonal levels comes off as major hyperbole to me and just another way misandrists like to play victim and blame their failures in life on imaginary issues.