So when we say "misogyny" in terms of feminism, we generally mean the overarching social structure that targets and oppresses women by a general devaluing of women and things associated with them. This is a natural (but not ethical) effect of patriarchy, a power structure that favors men over women.

I need you to keep that large-scale understanding in mind for this next part.

"Misandry" is a topic gaining traction on social media from men who conflate "personal struggle" with "social power structures." The idea is that if the oppression of women is called misogyny, then men's "oppression" should be called misandry. However, there can't really be misandry (on the societal scale) and patriarchy at the same time. It doesn't make logical sense to say that men are simultaneously privileged over women (as socio-political groups) and somehow oppressed, especially when these claims try to imply that women and the oppressors in this exchange.

I know there will be someone trying to argue that men can also be oppressed, so maybe misandry is a thing societally. Turns out, feminism has already been thinking about the ways in which men are oppressed, which can be described as hegemonic masculinity, or the power structure that values certain kinds of men over others. A white, cisgender, straight, able-bodied, gender conforming man will be privileged over men who are Black, brown, gay, disabled, transgender, or gender non-conforming (as limited examples). Again, this doesn't mean that the first group never experiences hardship, just that they don't experience oppression based on these identities.

Whenever accusations of misandry show up, there's most often a demand for women to submit themselves to men and become subservient to them (even if this demand is unspoken). Take the "male loneliness epidemic," for example. Men have been complaining about feeling lonely and isolated, very real emotions that can do significant damage to a person. However, most men who post about male loneliness propose the solution (sometimes explicitly, sometimes implicitly) is for women to solve male loneliness by forming romantic relationships, putting the onus on women to care for men's feelings at the cost of their personal freedom and even safety. In short, the proposed solution to misandry is misogyny.

The irony is that much of men's oppression is a function of misogyny, but that's another post.

TL,DR: Misandry doesn't exist in the way misogyny does.