I think that's a valid way of looking at Zuko and Azula's relationship. But the thing is that the relationship did not end up the way it did because the planets aligned and a owl cried as the clock struck noon, or something. The writers chose to give them the relationship, and then chose to play it out in a way that fell into very, very old negative stereotypes about women and power.
This same pattern has recurred millions of times in millions of different stories. They almost all have some internal rationale for it that's not just "she was a woman, so she went nuts." ("The scientist who genetically engineered her messed up." "They had to get her pregnant somehow or else there's no heir to the throne. There are like thirty more books in this series!" "She symbolized East Germany.") After a while I think it kind of stops mattering what that internal rationale is.
I'm not sure it's appropriate to say that the show is a critique of someone-wins-someone-loses as a way of thinking about conflict - I mean, I think we were supposed to be pretty happy that Aang and co. won! I don't think we were supposed to be sad that everyone couldn't win, given that certain segments of everyone were genocidal maniacs.
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This same pattern has recurred millions of times in millions of different stories. They almost all have some internal rationale for it that's not just "she was a woman, so she went nuts." ("The scientist who genetically engineered her messed up." "They had to get her pregnant somehow or else there's no heir to the throne. There are like thirty more books in this series!" "She symbolized East Germany.") After a while I think it kind of stops mattering what that internal rationale is.
I'm not sure it's appropriate to say that the show is a critique of someone-wins-someone-loses as a way of thinking about conflict - I mean, I think we were supposed to be pretty happy that Aang and co. won! I don't think we were supposed to be sad that everyone couldn't win, given that certain segments of everyone were genocidal maniacs.