the thing is that Katara's right.
there are a lot of episodes of ATLA where the main characters aren't totally right, because they need to learn a lesson about something. they're kids, it's a kids' show, there are morals to get across. that's not a bad thing; for the most part ATLA tells those stories really well without condescending its characters or its audience, which is why the cast gets to grow and change so organically and we're all still frothing about how good the writing is twenty years later.
but when Katara attacks that old man right there in public where everyone can see, she's right. this isn't a lesson about her needing to learn patience or humility or deference to her elders or respect for a belief system that's different than her own. in that moment Pakku is both the face of the Norther Water Tribe's cultural misogyny and an asshole who has disrespected Katara personally, and instead of having to find a way to play nice she gets to attack him with everything she's got.
she doesn't win. she can't win, it would be ridiculous. but the show knows this; Katara herself opens the scene by saying she doesn't expect to win while Sokka and Aang try frantically to talk her down. it's not about winning, it can't be. Pakku is, very literally, old enough to be her grandfather; he's had decades to master his form in a walled city untouched by war. Katara is 14 years old and the only bender from a village that's been diminished to nearly nothing. there's never been anyone to teach her; the artform died out before she was born. she has nothing. every scrap of knowledge she has is something she's had to struggle and steal for. how much of her waterbending has she learned on the fly, improvising as she fights desperately to keep herself and her friends and innocent bystanders alive? she's the Avatar's waterbending master, sure, but she's learning alongside him.
and she still gets to hold her own, for a few furious minutes. this old man doesn't even initially respond to her challenge, won't even dignify her by looking in her direction, treats her with scorn when he does finally address her. she is always, always at a disadvantage against him but she gets to make a scene, she gets to tear down entire structures, and she gets to be right. the fight ends with Katara immobilized in ice, completely outmatched, still seething and snarling at Pakku that she's not finished with him. she never backs down for a second, never doubts even for a moment that she has every right to beat this man's ass for the way he's disrespected her.
and the narrative backs her up on that, 100%. Katara is, frequently, unreasonably self-righteous to the detriment of herself and her friends, but this isn't one of those times. there's no moral for Katara to learn here; Pakku is the one who needs to get his shit in order.
a smug old man is a dismissive, sexist twat to a teenage girl who has suffered more than he will ever understand and when she sttacks him no holds barred she is framed as so completely, totally in the right that it's still cathartic two decades later as a woman in my late twenties. teenage girl moment of all time.