It could also be due to personal reasons related to his growth and self - discovery. The events of the Triwizard Tournament might make him realize that he needs to find his own path outside of Hogwarts for a while. He might feel that the school can't offer him the answers or the experiences he needs at that moment to become stronger and more independent.
Well, it might show Harry on a journey of self - reliance. He could be traveling alone, facing new challenges outside of the school's protective bubble. Maybe he meets new allies who help him understand the bigger picture of the magical world that Hogwarts had shielded him from.
Maybe he leaves because of a conflict with the Hogwarts staff. If the new headmaster or some teachers start implementing rules that Harry believes are wrong or unfair, like restrictions on defensive magic classes, he might decide to leave in protest.
One reason could be to search for a powerful magical artifact outside of Hogwarts that they believe is crucial for defeating a new dark threat. In fanfiction, they might feel that Hogwarts has become too dangerous or restricted in terms of resources for their mission.
Maybe the fanfiction portrays some really dark and disturbing events that make Harry feel he can't stay at Hogwarts anymore. For example, if it involves his friends being seriously harmed in the fictional story in a way that he can't bear to be associated with the place where it all seems to be happening.
He might leave Hogwarts in fanfic due to a sense of disillusionment. Maybe he discovers some dark secrets about the school or the wizarding world in general that make him question his place there. It could be something related to the way the school is run or a conspiracy among the teachers that he stumbles upon.
One possible reason could be to protect Teddy. Maybe there are some threats in England that Harry wants to keep Teddy away from. For example, there could be some dark wizards or dangerous magical creatures that target Teddy for some reason.
One possible reason could be that he feels constantly in danger at Hogwarts. With all the dark magic threats and attacks that keep happening, he might think leaving would keep his friends and himself safer. For example, after the Chamber of Secrets incident, he might have considered leaving to protect others from Voldemort's influence.
One reason could be a sense of self - sacrifice. Harry might think that by leaving the golden trio, he can keep them out of danger. For example, if he believes he is being targeted by a powerful dark force and doesn't want his friends to get hurt because of him.
One possible reason could be miscommunication. Maybe they had a big fight over how to raise their child and Ginny, feeling unheard, decided to leave. Another reason might be external pressure. For example, if some dark forces were targeting their family again and Ginny thought leaving would keep Harry and the child safer. Or perhaps Ginny had some personal issues she couldn't deal with while being in the family, like feeling she lost her own identity in the relationship.
One possible reason could be that he's tired of the constant danger at Hogwarts. There are always threats like Voldemort's followers or dark creatures lurking around. Another reason might be that he feels pressured by the expectations placed on him as 'the Chosen One'. Everyone expects him to save the day all the time, and it's a huge burden.