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.
Well, in some fanfictions, Natsu might drop out of Fairy Tail because he wants to protect the guild. He might discover a threat that is specifically targeting him within the guild, and he believes that leaving will draw the danger away from his friends. Also, it could be related to power. If he gains some new, uncontrollable power that he fears might harm the guild, he might choose to leave.
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 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.
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.
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.
One possible reason could be that he's framed for a crime he didn't commit. Maybe someone planted false evidence to make it seem like he was endangering the guild. Another reason might be that his power got out of control and the guild, fearing for the safety of its members, made the tough decision to kick him out.
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 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.
In a fanfiction, there could be a situation where Lucy is forced to side with a group that Natsu is against. This would make Natsu see her as an enemy. Or perhaps there is a prophecy that Lucy is involved in that Natsu misinterprets as something bad. He might think she is a threat to the guild or his friends. Also, if there is a love triangle situation where Lucy chooses someone else over Natsu in a way that really hurts his feelings, that could be a reason for him to start hating her.