There is a considerable overlap between misandry and misogyny. Things like gendered participation in society like a mens only draft is misogynistic because it posits that only men are of value in combat wartime defense but the issue does get muddier. Consider also alot of organized resistance to the draft for all American conflicts after WWII were actively participated in by women even though they were not directly effected. A lot of the social resistance to the conflict was female coded imploring to think in terms of social losses of sons, brothers and husbands in a plea to make men more humanized. The topic of having a draft at all regardless of whether it only effects men is generally unpopular demographically with women as a whole usually because they care directly for the welfare of men they know. So using that as any kind of "gotcha" isn't going to be recieved well.

Misandry as an issue is tied into gender politics in a weird way. It pushes aptitude for being capable of dangerous work and disruptive classroom behaviours as a masculine trait... But the buy in comes from all sides. A lot of the victims of heavy misandry are queer and gender non-conforming youth and guys who are told they are too emotional, quiet and cautious. The whole "alpha male" discussion for instance is peak misandry. Take other issues of gender bias is court custody cases that tend to paint men as victims of gendered bias but less than 1/3 of judges are female and there is evidence that gender bias cuts both ways regardless of the judge so while there are definitely things female judges should consider they are not the majority that needs to be spoken to.

On a lot of misandry related issues "the call is coming from within the house". Should we be looking at laws to combat misandry? Yes. Would these initiatives likely just be ultimately termed "woke feminizing indoctrination" by the right and be ridiculously unpopular with men demographically as a whole - also yes. Misandry comes in a lot of flavors not just the kind that comes in the forms disliked by "manly" men.

As a discussion point we as a society are in the infant stages of concensus on misandry. At the beginnings of the feminist movement a lot of misogyny came from inside the house too. Women were looking at other women with disgust at them being loud and brash and "man like". Treating their desire for expanded social roles as an affront to the delicate nature of correct womanhood and saying nonsense like "what man would ever want you" or claiming that behaving like men would impact their fertility. That's basically the genderflipped version of where we are now with a lot of men actually being quite on board with a lot of misandry.