It could also be that Katara was being overly critical of Aang's progress in learning new skills. Aang might feel frustrated and angry if Katara is constantly pointing out his flaws instead of being more encouraging, especially if he's already trying his best.
In some cases, the anger could be a catalyst for a more romantic development. Aang expressing his strong emotions might make Katara realize the depth of his feelings for her. Or it could be the other way around, Katara's reaction to his anger could make Aang see her in a new light, leading to a shift in their relationship dynamic towards a more romantic one.
It could be that the fanfiction writers wanted to explore a more complex and darker side of relationships. They might have written scenarios where Aang hates Katara due to jealousy, perhaps over her friendship with another character. This would add an interesting twist to the original relationship dynamics between them.
Perhaps Aang has a vision of the future where Katara is happier without him. So, in the fanfiction, he decides to respect that future and let her go.
In some fanfictions, it might be part of a plot to create tension. The writer wants to show that their relationship isn't all smooth sailing. So, Katara hurting Aang can be a device to make the story more interesting. It could also be related to different character arcs, like Katara trying to become more independent and in the process, her actions accidentally harm Aang.
One possible reason could be their different approaches to life post - war. Aang is the Avatar and has a whole world to look after, while Katara has her own tribe and personal goals. Their busy schedules might pull them apart. For example, Aang might be constantly traveling to different nations for diplomatic and Avatar - related duties, leaving Katara feeling lonely. Also, they might have different ideas on how to handle future threats. Aang may prefer a more pacifist approach which Katara might not always agree with, especially if it endangers the people she loves.
Perhaps Katara falls in love with someone else. In a fanfiction scenario, she might meet a new character who she feels a stronger connection with. This new relationship could cause her to break things off with Aang, shattering his heart in the process.
Their relationship could deepen as they share in the joys and sorrows of rebuilding the world. They've been through a lot during the war, and now they can truly rely on each other. They might become even closer friends at first, with a mutual respect for each other's abilities growing stronger.
The writer might be trying to add some drama to the story. By making Aang hate Katara, it creates a conflict that can drive the plot forward. For instance, their friends might have to work hard to resolve this hatred and restore their friendship.
Maybe in the fanfiction, Aang leaves Katara because of a misunderstanding. For example, he could misinterpret something Katara said or did regarding their relationship. This misunderstanding could lead him to believe that it's better for both of them if he goes away. He might think that he is protecting Katara in some way by leaving.
No. Fanfiction that involves sexual content about characters is not appropriate. These are fictional characters often aimed at a wide range of audiences, including younger viewers. Such fanfiction goes against the family - friendly nature of the original works and can also be considered disrespectful to the creators' intentions.