She may not like the false interpretations of Batman in some fanfictions. Fanwriters might change his personality or motives, and as a fellow hero, she doesn't appreciate that.
His connection with Gotham City. Batman has a deep and personal connection with Gotham, and the city almost seems to be an extension of him. In fanfiction, Wonder Woman, who is more associated with Themyscira, might envy this strong bond. She may feel that his relationship with Gotham gives him a unique identity that she lacks in relation to any particular place.
It could also be due to mind control. A powerful villain might have controlled Wonder Woman's mind and made her turn against Batman. In this scenario, Wonder Woman would act against her own will and kill Batman, creating a tragic situation in the fanfiction.
Naruto might dislike fanfiction because it can be a source of misinformation. Fans who read fanfiction might get the wrong idea about him or his world. He wants people to understand his story as it was originally intended. The original Naruto story is a carefully crafted narrative about ninja life, dreams, and the pursuit of peace. Fanfiction can deviate from this and make it seem like something else entirely, which he would find unacceptable.
One possible reason could be their different approaches to justice. Batman is more about vengeance and using his own set of rules in Gotham, while Wonder Woman comes from a place of more idealistic and Amazonian values of justice. Their clash in ideologies might lead to an argument.
Maybe Percy has a different set of values. He might be more into peace and stability rather than the chaos and violence often associated with the hunt. In fanfiction, the hunt could be depicted in a way that goes against his moral code.
One reason could be a misunderstanding. Maybe Batman suspects Wonder Woman of being involved in something she's not, like a potential threat to Gotham that he misinterprets. Another could be ideological differences. Batman is very much about justice in his own city, while Wonder Woman has a more global and myth - inspired view of justice.
Tony Stark may dislike Avengers fanfiction because it can mess with the emotional core of the team. The real relationships between the Avengers are deep and complex. Fanfiction might simplify or distort these relationships. For instance, his friendship with Steve Rogers has many layers, and fanfiction could make it into something that doesn't do justice to their real bond. Also, he's a man who values his privacy to an extent. Fanfiction might delve into his personal life in ways that he doesn't appreciate, making him feel exposed and misrepresented.
It's possible that he hates it because in fanfiction, his friends and he himself might be portrayed in ways that are completely different from who they really are. For example, Hermione might be made into a silly character instead of the intelligent and brave witch she is. This distortion of the people he cares about could be a big factor.
Lex Luthor could be a likely candidate. He is extremely intelligent and has a long - standing vendetta against superheroes. He might come up with a complex plan using his vast resources and scientific knowledge. For example, he could create a weapon that targets their unique abilities. He could also manipulate other villains and heroes alike to create a situation where Batman and Wonder Woman are isolated and vulnerable.
Batman might avoid Wonder Woman in fanfic because he's afraid of getting too close to someone with such strong emotions. He's used to suppressing his own feelings, and Wonder Woman is very passionate. Her presence could stir up emotions in him that he doesn't want to deal with in the fictional stories.