Perhaps Jarvis hates it because it can create false expectations or rumors about the Avengers. Since he is part of their inner circle in a way, he doesn't want inaccurate ideas to spread. For instance, if a fanfiction implies a romantic relationship between two Avengers that is completely untrue in reality, it could cause unnecessary confusion.
In some fanfictions, Peter could have a secret that he's keeping from the Avengers. When it's eventually revealed, they might feel betrayed and turn against him. It could be something related to his powers, or his past associations that the Avengers find unacceptable, thus resulting in their hatred.
Differences in ideology can also play a part. Tony might have some views on how to handle threats or use technology that the other Avengers don't agree with. Maybe he's more willing to take risks with untested tech that could endanger the team or civilians, which would lead to resentment.
One possible reason is that Peter's quick rise to popularity among the public might make the Avengers jealous. They've been around for a long time, and suddenly this young kid is getting all the attention.
Perhaps Tails feels that fanfiction undermines the hard work of the original creators. He might think that the official story should be the only source of information about him and his adventures, and fanfiction is an unwanted deviation from that.
One reason could be that he doesn't like how some fanfiction writers misinterpret his character. They might make him act in ways that are completely out of character in relation to Renesmee. He has a certain image of himself and his relationship with her, and fanfiction can mess that up.
One reason could be that he was treated unfairly by other shinobi. If he was constantly looked down upon or discriminated against by his fellow shinobi, it might make him develop a hatred for them.
It's possible that the writer of the fanfiction has given Akeno a backstory or personality trait that directly clashes with Naruto's. Maybe she is extremely arrogant and Naruto, who is humble and believes in everyone's potential, would find that detestable.
It might be due to the way their goals are presented in fanfiction. Naruto is often about protecting his village and friends. If Artemis's goals in the fanfic are in conflict with Naruto's, like if she's more focused on her own self - interest in the story, Naruto would hate her.
One possible reason is that Naruto is so focused on his ninja training and his goals in the shinobi world that he views Christmas as a distraction. He might think it takes people's attention away from more important things like self - improvement and protecting the village.
Jiraiya was a serious shinobi with a certain code. Fanfiction might play around with that code too much for his liking. It could make light of things he held in high regard, like his loyalty to the Leaf Village or his training of Naruto. So that's a possible reason for his hatred.