In the fanfic, it might be that Quagmire spread false rumors about Brian in the town. Brian hears about these rumors and confronts Quagmire. When Quagmire doesn't take it back or apologize, Brian snaps and beats him up. This then causes a rift in their friendship (if they can call it that) and the fanfic could explore how they either repair it or go their separate ways.
Well, it could be that Quagmire did something really offensive to Brian's owner, like constantly hitting on Lois in a very vulgar way. Brian, being protective, decides to take matters into his own paws and beats up Quagmire to teach him a lesson.
Maybe Quagmire made a cruel joke about Brian's failed attempts at writing. Brian, who is already frustrated with his lack of success, loses his temper and starts to beat up Quagmire. This could lead to a series of events where the whole neighborhood gets involved, some taking Brian's side for standing up for himself and others thinking he went too far.
Perhaps Quagmire insulted Brian's intelligence. Brian is often portrayed as an intelligent dog, and if Quagmire kept making snide remarks about his intellect, Brian might reach a breaking point and lash out at him. In a fanfic, this could be a great source of drama and conflict.
Maybe Sasuke says something really offensive about their past or her skills, and Sakura just snaps and starts beating him up.
In this fanfiction, perhaps there is a misunderstanding between Luke and Percy. Luke might think Percy has betrayed him in some way, like siding with the wrong people in the context of their fictional world, and thus resorts to violence by beating him up.
Maybe Sakura gets angry at Naruto for some misunderstanding, like he accidentally ruins one of her important medical experiments. So she decides to beat him up to teach him a lesson.
Perhaps in the fanfiction, Percy is under some sort of dark influence. This could be from a new, unknown magical force. This influence makes him see Jason as a threat to his friends or himself, so he attacks Jason. Jason, on the other hand, is initially confused but then tries to fight back to defend himself while also trying to figure out what's wrong with Percy.
Well, it could be about a young hero's journey. Maybe Torentos Brian adopts a character who has special powers but doesn't know how to control them. Brian then helps this character to learn about their powers and use them for good in a world full of challenges.
The plot could be simple. Maybe Brian accidentally discovers that he is extremely ticklish. And his friends or family members find out about it too. They start to playfully tickle him, which leads to a series of comical events. For example, he tries to escape but fails miserably.
Well, in such a fanfiction, perhaps Sasuke has some sort of plan that involves Hinata in a negative way. Naruto discovers this and decides to beat up Sasuke to protect Hinata. It could also be part of a bigger struggle where Sasuke's actions are seen as a threat to the future Naruto envisions with Hinata, so Naruto takes matters into his own hands to stop him.
Perhaps Naruto is under the influence of some sort of ancient and uncontrollable power. This power makes him extremely aggressive and strong. Kakashi tries to stop him but is no match for this new - found strength of Naruto. As a result, Naruto beats Kakashi senseless. Another plot could be that Kakashi is injured before a fight with Naruto and Naruto, not realizing how badly hurt Kakashi is, uses his full strength and ends up beating him senseless.
One possible reason could be a misunderstanding. Maybe Sakura makes a decision that Naruto strongly disagrees with regarding the safety of the village or their friends. For example, if Sakura decides to trust an enemy without Naruto's knowledge, Naruto might get so angry that he lashes out at her.