personal opinion but thinking about it now. i do also think the Nanami Cow Episode is both like. intentionally silly goofy weird and maybe not as suuuuper deep as some people make it out to be, but there are *some* things i think we can genuinely take from the episode. maybe less as a general statement about patriarchy as a whole and more about the characters (namely, nanami/anthy) and how *they* react to the patriarchal overtones of the setting. does that make sense?
like, i don’t think nanami’s fear over becoming a cow that then gets butchered for meat and eaten by her brother is a statement about how all women feel in society, but instead is very specific to her relationship with touga. she’s afraid that he doesn’t see her as someone special to him, that she won’t always have his affection. if she somehow does something to mess things up (embarrass him, fade into the background, etc) then she becomes inhuman and unimportant—or alternatively, something to be mocked. if she can’t establish herself in a forever Little Sister role, then she becomes yet another woman for touga to consume and forget about. also, she’s like 13 and wants to look cool in something *designer* (status symbol) but unfortunately she’s not very smart lmao.
anthy, as the person who causes the whole cowbell shenanigan, is using her influence over ohtori (and nanami specifically) to assert power in a setting where she is frequently denied agency. she intentionally sets up humiliating scenarios for nanami, probably for equal parts entertainment and resentment. she *cannot* fuck with the men in her life that have hurt her the most and so she goes for the easier target: a girl who reinforces the oppression *anthy* has to go through by slapping her, by trying to publically humiliate her at the dance. both nanami and anthy are girls who objectively get treated like shit by the people they devote themselves to, so a fun little reprieve for them is to hate each other as narrative foils.
that being said i have no fucking clue what’s up with the nanami cow scene in the movie.