One possibility is that Hestia took away something important from Percy in the fanfiction. It could be a magical item or a chance to achieve a great goal, which made Percy resent her.
Perhaps in the fanfiction, Hestia sided with Percy's enemies for some reason. This betrayal, whether real or perceived, would surely make Percy hate her.
Perhaps the hunters always interfere in Percy's adventures. They might show up at the wrong time and disrupt his plans. For instance, Percy was about to rescue someone, and the hunters came and took over, but in a way that put the person in more danger. This would make Percy resent them. Also, if the hunters have some internal politics that end up affecting Percy negatively, like they accuse him of something he didn't do just to protect their own reputation, that could lead to his hatred.
Maybe he got into a big fight with his friends during Christmas. It could be that they had different ideas about how to celebrate or some misunderstanding that made him sour on the holiday.
In fanfiction, it could be that the Third Hokage favored certain ninja over Naruto for no good reason. For instance, giving more resources and opportunities to others while Naruto had to struggle on his own. This unfair treatment might be a reason for Naruto's hatred.
One consequence could be that it divides the fan community. Fans who like Jason might not appreciate Percy being portrayed as hating him, and vice versa. This could lead to arguments and a split in the fandom.
One consequence could be that he might face social isolation in certain situations. For example, in a party or gathering where alcohol is the main feature, Percy would be the odd one out, which could lead to him being excluded from certain social circles within the fanfiction.
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 the fanfic, it could be that Kami has a conflict with one of Naruto's allies, and Kami's actions against that ally make Naruto angry and lead to his hatred. For example, if Kami tries to punish Naruto's friend for no good reason, Naruto would not be happy with Kami at all.