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.
Perhaps in the fanfiction's plot, Natsu makes a big mistake that endangers Lucy or her friends. Let's say he recklessly takes on a powerful enemy without a proper plan, and Lucy's friends get hurt as a result. This might cause her to hate Natsu for his irresponsible behavior.
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 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.
Maybe she just lost interest in the Fairy Tail world. Fanfiction can be a passing fancy, and her enthusiasm might have waned over time.
There might be a lot of bad writing in the fanfiction that involves Natsu. Poorly written dialogue, actions that don't make sense for his character, or just a general misrepresentation. If the fanfiction is full of these elements, it could give the impression that Natsu hates in that fictional world created by the writer, even though it's not true to his real character.
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.
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 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.
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.
One possible plot twist could be that Lucy initially refuses Natsu's proposal because she fears it will change their dynamic in the guild. She might think that getting married will make them less focused on their adventures and more on domestic life.