One possible reason could be that the Cullens make a decision about her future without consulting her. For example, if they decide she should leave Forks for her own safety without asking her how she feels about it.
She might start by giving them the silent treatment. Just ignoring them completely when they try to talk to her, which would be a very human way of showing anger.
One possible reason could be that Erza might have taken on a dangerous mission alone without informing Natsu. Natsu is protective of his friends and would get angry if he thought Erza was putting herself in unnecessary danger.
One possible reason could be that Videl does something that endangers herself. Gohan, being protective, might get angry out of fear for her safety. For example, if she recklessly jumps into a fight without proper training or preparation.
Well, it could be due to the way the Cullens interact with the other people in Forks. If Bella notices that they are being manipulative or using their powers in a way that she doesn't like to influence the townspeople, that could make her start to hate them. Also, if there is some kind of power struggle within the Cullen family that starts to affect Bella negatively, like she gets caught in the middle of it or she sees how it's causing harm to those she cares about, she might turn against them.
It could be due to a misunderstanding. Perhaps someone spread false rumors about him, and as a result, people started treating him differently. He might be angry at everyone because he feels that no one bothered to find out the truth from him. Also, if there were some new rules or restrictions imposed on him without proper explanation, that could fuel his anger.
One possible reason could be Edward's over - protectiveness. He often tries to shield Bella from danger in the Twilight series, but in fanfiction, this might be taken to an extreme that annoys Bella. For example, if he constantly stops her from doing normal things like going out with friends or pursuing her hobbies without proper explanation.
One possible reason could be that she discovers some dark secrets about the Cullens. Maybe she finds out they have been lying to her about their true nature in a more malicious way than in the original story. Another reason might be that she feels threatened by their vampire powers. If they accidentally or purposefully use their powers around her in a menacing way, it could make her feel scared and turn that fear into hatred.
Maybe she was betrayed by someone she trusted. In many stories, a betrayal can easily make a noble character angry.
His family might have neglected him in some ways. Naruto grew up alone and feeling unwanted in the original story. If in the fanfiction, his family was around but still didn't give him the love and attention he needed, it would be a valid reason for his anger. He has always craved connection and acceptance, and if his family failed to provide that, he would be furious.
It could be that she has some special power she's been hiding all along. Maybe she can communicate with animals secretly and she's been too afraid to tell the Cullens before.