I think some ppl are being disingenuous about the fact that a big part of why Zutara is hated with that level of vitriol is because of misogyny. It is a ship that falls into tropes that appeal to women. The way zk antis talk about the shippers reeks of misogyny.
The way Bryke discusses them reeks of misogyny. They literally said in a room full of young teens that girls who ship Zutara would end up in abusive relationships because Zuko's a “bad boy”. Their overall behavior towards the ship, and to some extent Zuko, screams of misogyny.
The way Katara's possible role in the dynamic is framed by antis reeks of misogyny. The portrayal of how Aang feels towards the possibility of those two being a couple, both in canon and in fandom, reeks of misogyny.
And the misogynistic vitriol becomes more potent when Zutara, in terms of popularity, sits right next to a ship that has a lot of male-centeredness & self-insertion in its writing. As lovable as Aang is, the way he's written, romance-wise, does fall into negative tropes. I mean, there is a reason a lot of dudebros are drawn to that ship over Zutara, Taang, and Sukka despite hating Katara to the moon and back.
