It could be because of a conflict with the academy's rules. Natsu is a bit of a rebel. If the academy has strict rules that go against his sense of justice or freedom, he might decide to drop out. For example, if they forbid him from using his dragon - slayer magic in a certain way. Another reason could be that he feels he can learn more on his own or from other non - academy sources. He might think that the real - world experiences and challenges are better for his growth as a wizard than staying in the academy.
One possible reason could be a conflict with other guild members. Maybe there's a misunderstanding or a fight that makes Natsu feel he no longer belongs. Another reason might be that he has a personal mission that goes against the guild's rules or values in the fanfiction. He could also be framed for something he didn't do and, feeling betrayed, decides to drop out.
I'm not sure of specific 'natsu drop out of fairy tail academy fanfiction' stories off the top of my head. But you can try searching on fanfiction websites like FanFiction.net or Archive of Our Own. They usually have a wide variety of fan - created stories based on different themes and characters from Fairy Tail.
One reason could be that the fanfictions don't match his view of the Fairy Tail world. He has his own understanding of the guild, his friends, and their adventures, and when fanfictions deviate from that, he doesn't like it.
Perhaps Natsu is under the influence of a powerful and dark magic that makes him lose control of himself and accidentally hurt Lucy. It could also be that Natsu is trying to protect Lucy from something but his actions end up causing her harm instead. Like if he tries to keep her away from a dangerous situation by pushing her too hard and she gets injured.
One reason could be that the fanfiction author is trying to create a new and edgy storyline by making Natsu a more negative character. But this often doesn't sit well with fans who love the original positive and passionate Natsu.
They could leave for a quest of self - discovery. Natsu might want to learn more about his past, especially about his dragon, and Juvia could be looking to find out more about her water magic's origin. So they leave Fairy Tail to explore different places and meet various mages who might have the knowledge they seek.
Perhaps Natsu feels betrayed by the guild first. There could be a situation where he believes the guild has turned its back on one of his closest friends or on a principle he holds dear. This sense of being let down by the guild might lead him to take extreme actions that seem like betrayal. It could also be related to a power struggle. If there's a new power within the guild that Natsu sees as a threat to the guild's original values, he might try to oppose it in a way that looks like betrayal from the outside.
One possible reason could be a misunderstanding within the guild. Maybe someone spreads false rumors about Natsu, leading others to believe he's done something wrong. Another reason might be a power struggle. If there are those in Fairy Tail who envy Natsu's strength and popularity, they could plot against him to get him out of the way.
One possible reason could be to seek new adventures. They might feel they've reached a point in Fairy Tail where they've done all they can and want to explore new magic and challenges elsewhere. For example, they could have heard of a far - off land with a different type of magic that they are eager to learn about.
Maybe he got into too many fights. Natsu has a short temper and if there were other students in the academy who provoked him or if he was standing up for someone, he might have engaged in brawls that the academy doesn't tolerate. In a place like Fairy Tail Academy, they might have strict rules about student behavior regarding fighting.