Honestly, I feel like there are a variety of reasons as to why Kataang is continuously misunderstood/analyzed. The most obvious one, and the one from which most other things stem, is that people just don't like the idea of Aang as the love interest. To them, he isn't what a typical male love interest looks like, so they can't imagine why Katara would ever want to be with him when someone who looks like Zuko exists. This isn't just about people who ship zk, either. There are plenty of people who saw that Katara had a crush on Jet and then just decided that was her type, and that she could never fall for Aang because of that. I honestly think it's hilarious, too, how people will bend over backward to explain why they ship Katara with people who aren't Aang—and yes, it is mainly zk fans that I have experienced doing this—but will then just attribute a bunch of stuff that is canon to Kataang to the other ship. Just say you don't think Aang is attractive and leave.
As an extension of that, since people cannot fathom Katara liking Aang romantically, they willfully ignore the signs that Katara is interested in him the way he is in her. They rewrite it as her being motherly towards him, despite clear evidence in the show that Katara treats Aang differently than she treats anyone else. Yes, she supports him emotionally, but he does that for her, too. People just choose to ignore what he does for her or take his actions out of context in order to justify the idea that they have a one-sided relationship where Katara takes on all the emotional labor and Aang is nothing more than a child who pines after Katara and forces her to take care of him.
There is also just a lot of warping of who Aang and Katara are as individual characters. Yes, Aang is a goofy little kid, but he is also a wise and experienced bender, and he has shown time and time again that he has the emotional maturity to handle being THE AVATAR at just 12 years old. Yes, Katara is motherly, but she is also just a kid who likes to have fun and laugh, and she HATES that people don't see her that way. These people don't truly understand the characters in the show, and instead, they self-insert. So, rather than looking at Katara's actions through the lens of who she is as a character and what she wants, they think about what they would want, and that doesn't align with the canon. Something that, for me, further proves the first point I made that also ties into this one is how when Katara shows kindness and empathy to Zuko, it is immediately perceived as being romantic despite it being very in-character for Katara to do, but when she treats Aang the same way, she's being motherly. They like the way Katara and Zuko look together more, so when the 2 of them interact, it's chemistry. But when Katara cups Aang's face lovingly, kisses him on the cheek, or hugs him, it's "mother-son" because it's not visually appealing to them.
That ties into one of my last points—and I have an entire post on this already that you probably read—which is that people are expecting Kataang to have out-of-this-world, mind-blowing chemistry when they are just children. Their relationship is soft and sweet, and more importantly, their friendship is the basis for their romance. Of course, their relationship feels more like a friendship for a majority of the show; THEY'RE BEST FRIENDS. That has always been their core. The progression is supposed to be us watching as these 2 children find each other and recognize parts of themselves in the other in a way that no one else can and develop a friendship that later blossoms into love, at least what love can be for a 12 and 14-year-old.
My final point is that AtLA isn't a show about romance to being with, so, while there is romance interspersed throughout the show, it is a subplot. They don't want to spend as much time building a romance as they do the main story, which makes sense. I will say that I personally still think that they did a good job of building the romance, and that season 3B is really the only place where I feel things could have been better written. However, I think it's just willful ignorance to say that Katara and Aang not interacting a significant amount in the last episodes means that their relationship was "rushed" or "forced". There is still a whole 2.5 seasons worth of build-up at that point, and it's pretty obvious from episode 1 that Katara and Aang have a special connection.
As for the kiss in EIP, it was definitely meant to show the "will they/won't they" nature of Kataang's relationship and to cause drama/tension for the fans. I don't think it was necessary, and it could 100% be taken out, but even with it still in the show, I don't think it's something that breaks Kataang as a ship. It was not okay that Aang kissed her when she said she was confused, but she calls him out, and he recognizes that he messed up. It's not brushed over and just ignored in the moment. He is also 12 and prone to making mistakes, and while it is a big one, I do not think it deserves the vitriol that certain portions of the fandom treat it with. Once again, it is actively addressed in the narrative that he was wrong to do that (he also course corrects later in the comics). Do I wish they could have had just even 1 more one-on-one interaction before the final kiss on the balcony? Sure, but I am also able to understand that a significant portion of time has passed between the 2 scenes and I can suspend my disbelief enough to think that they talked it out or that it was at least something apologized for and forgiven.
This is a lot longer than I expected it to be, but what I really think it boils down to is a.) lack of media literacy and b.) people being upset that what they wanted didn't happen, and rather than recognizing that they are allowed to have an opinion that differs from canon, they will do anything they can to rewrite it so that they can feel vindicated in choosing the ship that they chose. They need it to be canon rather than allowing it to remain headcanon. There has also been a lot of misinformation spread about who the endgame ships were originally intended to be, and that truly set us back as a fandom because people still believe those things to this day, even after it has all been disproven multiple times.
