Maybe Chi - chi is constantly comparing Gohan to Goku in the fanfiction. Gohan has his own identity and abilities, and being compared all the time can be frustrating. He could get mad because he wants to be recognized for who he is, not just as Goku's son. Also, if Chi - chi is interfering too much in his training or friendships, that could also lead to his anger.
Another possibility is a jealous rival. Maybe there's someone who is jealous of Gohan's power or his relationship with certain characters. This rival could do things to annoy Gohan and push him to the edge of his temper.
One reason could be ChiChi's overbearing nature. She is often very strict about Goku's training and how he spends his time. In fanfiction, this could be exaggerated to the point where Goku finally gets fed up. For example, if she constantly nags him about not doing enough chores around the house instead of training, it might push Goku to his limit.
Maybe Tails was tinkering with Sonic's shoes or some other personal item without permission. Sonic values his stuff and his independence. If Tails was messing around with his things in an attempt to 'improve' them but instead caused a problem, Sonic would likely be angry.
One possible reason could be if Naruto in the fanfiction is being unfaithful to her. In the original series, their relationship is built on trust and love. So, if the fanfic portrays Naruto in a way that goes against that, Hinata might get mad.
Perhaps Percy forgets an important promise he made to Annabeth. In their relationship, promises are significant. If he fails to keep one, like a promise to help her with a project or be at a certain place at a certain time, Annabeth would surely be mad. It could also be that Percy accidentally breaks one of Annabeth's creations or possessions, which she holds dear.
It could be due to unfair treatment from teachers. For example, if he's blamed for something he didn't do just because he's a Saiyan or has special powers. Teachers might be prejudiced against him, which would lead to his anger. He's a good - hearted person but constantly being misjudged would surely get on his nerves.
Well, maybe Gohan gets angry because Hercule takes all the credit for saving the world when in fact Gohan did a lot of the real work. In fanfiction, the writer might play up this injustice, making Gohan seethe with anger at Hercule's false bravado.
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.
In the fanfiction, Beast Boy could have eaten all of Raven's favorite snacks without asking. This simple act of thoughtlessness might set her off. Or he could have interrupted her meditation multiple times, which is very important to her. Also, if he was being too over - confident in a situation where Raven knew they needed a more careful approach, his cockiness could be a reason for her anger.
In some fanfictions, Sakura may make decisions without considering Naruto's opinion. Naruto values his friends and their input, so if Sakura goes ahead and does something like endangering the team or making a big decision on her own that affects everyone, Naruto could get mad. Also, if Sakura were to insult Naruto's dream of becoming Hokage, that would definitely be a reason for his anger as that dream is very important to him.