Hold the phone-- his primary reasons for liking Katara have to do with her being his very first contact in a foreign world where all his people were wiped from the face of the earth, and being supportive on top of that.
...and, yeah, because she's pretty, I guess.
Oh yeah, that’s why when it came to The Guru scene - the part that should’ve been the culmination of everything they’ve been through, that’s meant to really hammer home the weight of the importance going into his decision, how one person supposedly means so much to him that he’d be willing to trade phenomenal cosmic power to keep her - the imagery they use to portray this is not the "we’re your family now" scene, not all those times Katara pulled him out of the Avatar State, not their time in the desert where he was total prick to her the entire time and she treated him with more patience and understanding than most people would’ve realistically allotted him in that kind of life-or-death scenario (which he never acknowledges afterwards), not even some of her own character moments that didn’t directly involve Aang like the Pakku fight or the earthbender prison break to maybe show he admires her outside of the things that benefit him, but the animu sparkle beauty pan from the fortune cookie episode, right? To showcase all those personality traits he‘s interested in?
Truly, the bedrock of a romance for the ages.
Also, from I’ve gathered from talking to female fans in real life, even a lot of the Kataang shippers, the whole "using a girlfriend as a therapist/surrogate/coping mechanism for the lost of an entire civilization" thing isn’t considered one of the positives; to them it sounds emotionally daunting and unhealthy, or at best an internal conflict to be overcome. Codependency doesn’t exactly get the blood rushing south.
Her interest had to do with the fact that he was the ray of hope she had been hoping for her entire life, having been born into a war that claimed her mother's life, robbed her of her father, and ultimately decimated her society. Aside from that, Aang did plenty of comparatively trifling things for her, on top of doing the whole listening and empathizing/taking action thing you were talking about earlier.
...and, yeah, because he's God incarnate or something, I guess.
I mean, Katara liking him because of what represents is still only liking him based on what he is rather than who he is, and the most common piece of romantic advice Aang is given is that being the Avatar means he can have any girl he wants; there’s even a moment where someone tells him that Katara will simply "come around" because he‘s the Avatar, so how could she say no to him? Emphasizing that he’s a god incarnate, as though that should be a factor, kinda proves my point in that regard. That’s the sort of approach to romance most writers would attribute to antagonists like Gaston, not the story’s paragon of righteousness.
And thing is, other aspects of the the show often contradict the idea that idea. Two of the major themes in the story is that the definition of inner strength is giving yourself hope when nothing else in the world will, and that "destiny" is determined not by belief but through actions driven by self-discovery. This actually a common thing in Katara’s own arc, since she’s often the one motivating Aang and others rather than Aang giving her motivation, and more often than not the story rewards Katara for having faith in herself and/or her fellow man than she is for having faith in Aang specifically. There’s even several instances where it’s shown that The Avatar being back isn’t enough to motivate people to action like in Imprisoned, or Aang is serving as an obstacle conflicting with her hope like in The Desert, The Serpent’s Pass, The Awakening, or arguably even the finale. Hell, one of the most interesting parts of the finale’s subplot is that when history has seemingly repeated itself with Aang having vanished when he’s needed the most, the conclusion the others come to is that they can’t worry about whatever Aang’s doing, and instead have to focus on what they can do for themselves because determining the fate of the world will come down to everyone doing their part rather than the actions of one person - you can even see this at work looking at the previous finales where majority of the time the pivotal turning points in battle are often brought about by people other than Aang like Yue’s sacrifice or Zuko‘s joining the fray in the catacombs. I’d even argue the contradiction can be summed up in the fortune cookie episode since the majority if it is about accepting instances where your love/crush is unrequited (complete with direct parallels between the girl crushing on Aang and how Aang treats Katara) and that you shouldn’t put so much stock into prophecies or what others tell you what your destiny should be (it’s even a running gag throughout that Katara is doing exactly this to the point she’s doing things she doesn't want to) only to swerve hard at the last second to go "oh look this vague description arbitrarily matches Aang, so Aunt Woo was actually right all along!" I feel like if your main couple‘s getting together has to against the grain of the message of your own show, then something has gone wrong.
I’d also disagree that listening is a major aspect of Katara and Aang’s dynamic. Katara tends to talk about her mother a lot, but there’s a notable difference in how she talks about it with Aang, where the focus is usually in making him feel better rather than helping her sort out her problems, compared to how she talks about it with every other character like Sokka, Haru, Zuko, and her dad (which funnily enough comes about specifically because Aang ditching her causes her to spiral). The closest is maybe The Southern Raiders, but there Aang scenes only leave her frustrated and this conflict doesn’t get resolved by the end since they never end up seeing eye-to-eye. It paints a picture where Katara is usually Aang’s confidant, but Aang is never one for her.
