One possible reason is that their personalities clash. Percy is often portrayed as a more outgoing and confident character, while Nico is more introverted and brooding. In a fanfic, this could lead to misunderstandings and animosity between them. For instance, Percy's bold actions might seem reckless to Nico, causing him to dislike Percy.
One reason could be jealousy. Maybe in the fanfic, Annabeth gets more attention or praise for her skills and Percy feels left out or overshadowed, which turns into hatred. Another possibility is that there's a rift caused by their different approaches to solving problems. If Annabeth's logical thinking clashes too much with Percy's more instinctive ways, it could lead to resentment.
They could fight due to a prophecy. If there's a prophecy that involves one of them being the 'chosen one' and the others think they should be, it would create a lot of tension. For instance, if the prophecy says that only one of them can save the world from a certain doom. Percy, being the main character in many stories, might be assumed by the others to be the one, but Thalia and Nico may believe they have just as much right. Their struggle for that role could lead to a fight. And during the fight, they would use their unique abilities. Percy would call upon the water, Thalia would summon her lightning bolts, and Nico would raise the dead to fight on his behalf.
It could also be that in the fanfiction, Percy is given a new power or ability that Annabeth sees as a threat. Or perhaps Percy is made to side with someone Annabeth dislikes, causing her to 'hate' him in that fan - created story. This shows how different plot elements in fanfiction can change the dynamics between characters.
It might be that in the fanfiction, Calypso represents something that Percy has come to dislike. Maybe she is associated with a force or an idea that Percy opposes, like a form of confinement if she tries to keep him on the island in a more extreme way than in the original tales.
In fanfiction, the politics and intrigues within Olympus might be depicted in a way that makes Percy disgusted. The backstabbing and power - hungry nature of some of the Olympians could be too much for him to bear, so he hates Olympus.
Perhaps the fanfiction is set in an alternate universe where something has happened to change Percy's feelings towards Annabeth. For example, if there was a betrayal in the fan - created story that made Percy turn against her.
In some fanfics, there could be a misunderstanding. Suppose Kushina did something that Naruto misinterpreted as harmful to him or his friends. This misinterpretation could lead to his hatred. For example, if Kushina was involved in a mission that Naruto thought put the village at risk, but in reality, she had no choice.
One reason could be that the fanfic changes the essence of their relationship. In the original, they have a certain dynamic that she values, and fanfics might mess it up.
One reason could be jealousy. If Percy starts paying more attention to the child than to her, she might start to resent the child. It's a common trope in stories where a new addition to a relationship, like a child, can cause jealousy issues.
One possible consequence is that it could lead to a split in their group. If they are part of a team or a community, their animosity could cause others to take sides, creating factions.