Another aspect could be that the fanfiction writer wants to deviate from the typical positive view of Natsu in the original series. They might want to show his flaws in a more extreme way. So they write a scenario where his impulsive nature gets him into a lot of trouble and causes other characters to hate him. His hot - headedness could lead to him making decisions that negatively impact the guild or other characters in the fanfic.
One reason could be that some writers might want to create a more complex or darker storyline. By having Natsu be hated, it adds conflict. Maybe they portray him as having made a big mistake that the other characters in the fanfic can't forgive.
In some fanfictions, the author may be exploring different character dynamics. If they decide to make Natsu hated, it could be to show how the Fairy Tail guild would react to one of their own being an outcast. It could also be related to a power struggle. For example, if Natsu becomes too powerful too quickly, some characters in the fanfic might start to resent him, leading to hatred.
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.
The end might be hated because it didn't tie up all the loose ends properly. In 'Fairy Tail', there were many sub - plots and relationships. If the fanfiction end fails to address these in a satisfactory manner, like leaving a potential romantic relationship in an ambiguous state or not fully explaining a character's growth, fans would be disappointed.
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 possible reason could be a misunderstanding within the guild. Maybe some false information was spread about them, leading others in Fairy Tail to turn against them. Another reason might be a power struggle. If Natsu and Erza were becoming too powerful, some jealous members could have conspired to make it seem like they were betraying the guild. Or perhaps an outside force manipulated the situation to drive a wedge between them and the rest of Fairy Tail.
Perhaps they leave because of a disagreement within the guild. Maybe there's a new policy or a decision made by the guild master that they don't agree with. For example, if the guild decides to get involved in a war that they think is unjust, they might choose to leave rather than participate against their beliefs.
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.
One possible reason could be that he was wrongly accused of a serious crime within the guild. Maybe some powerful and influential members believed he was a threat and pushed for his banishment. For example, if there was a string of mysterious attacks and Natsu was framed as the culprit due to his often wild and uncontrollable nature in battle.
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.
He might become more withdrawn. Since he is used to being liked and part of the group, being hated could make him isolate himself from the others in the guild in the fanfic.