Maybe he has different views on the characters. He might think that fanfic often distorts the original image of Edward he has in mind, so he hates it.
Edward might hate Renesmee fanfiction because he has a very strong sense of self and his relationship with Renesmee. Fanfiction is written by many different people with different ideas. Some of these ideas could be completely contrary to what he believes and feels. It's like someone is taking something very personal to him and changing it according to their own whims. Also, he may be worried about how these fanfictions could influence Renesmee's perception of herself or their relationship as she grows up.
Another reason could be the influence of other characters. There might be a new character in the fanfiction who convinces Bella that Edward is not who she thought he was. This new character could plant seeds of doubt in Bella's mind about Edward's intentions and actions, ultimately resulting in her hatred.
Redemption can also be a theme. They both have made mistakes in their journey, and fanfics may explore how they try to make up for those mistakes. They might seek forgiveness from each other or from the people they've wronged, all while strengthening their bond as brothers.
He can simply avoid reading it. Just stay away from any fanfic related to Edward and focus on the original work or other things he likes.
One characteristic is the expansion of their personalities. In fanfiction, we might see more of Edward's determination in different situations or Alphonse's kindness and wisdom. Another aspect is the world - building. Some fanfictions create new places and alchemy - related concepts around Edward and Alphonse. Also, the relationship between the two brothers is often deepened, showing their unwavering support for each other in various challenges and adventures.
In some fanfics, Bucky might be written to hate Steve due to misinterpretations or plot twists. Maybe the writer wants to explore a darker, more conflict - ridden relationship. It could be that Bucky has been brainwashed in the fanfic and his altered mind now sees Steve as an enemy, or there could be some past event that was misconstrued and led to this hatred.
Perhaps Harry has his own vision of Gryffindor and the fanfics he's seen don't align with it. He might have a deep - seated understanding of what Gryffindor means to him, like courage, loyalty, and friendship in a very personal way. The fanfics, on the other hand, might focus on more superficial or inappropriate aspects of Gryffindor for his taste, such as focusing too much on power plays or false bravado rather than the true essence of what makes Gryffindor great.
Well, it could be that in the fanfic's storyline, Bella has had some bad experiences in the past related to intimacy. Maybe she was betrayed or hurt, which made her develop this hatred.
In the fanfic, Naruto could hate Team 7 because of a change in the story's plot. Perhaps something bad happened that he blames on the team. It might be that the team made a decision that Naruto strongly disagreed with, like a mission choice or how they treated an enemy. This could cause his feelings towards them to turn sour.
In some fanfics, Bonnie might hate Elena because of jealousy. Maybe Elena always gets the attention of the male characters they both know, like Stefan or Damon, and Bonnie feels left out or second - rate in comparison.