Jealousy could also play a part. For example, if Harry starts getting closer to other mentors or friends, Sirius might feel left out and act out in a way that causes a fight. Or if Sirius seems to be spending more time on Order of Phoenix business than with Harry, Harry could feel neglected and start an argument.
It could be due to a misunderstanding about their respective roles in their group or in a mission. For example, if Sirius thought James was taking too much of a leadership role without consulting him, it might cause a rift. In fanfiction, the writer might explore how their strong personalities clash in such situations.
In fanfiction, Sirius and Remus could fight over Hermione because of their different relationships with Harry. Since Hermione is Harry's close friend, Sirius might think that he should have more influence over Hermione to help Harry better, as he is Harry's godfather. On the other hand, Remus, being Harry's former teacher and friend, also feels a sense of responsibility towards Hermione because of her connection to Harry. This clash of responsibilities and their own personal feelings for Hermione can spark a fight.
One reason could be a difference in their approaches to justice. Batman is often more brooding and strict, while Nightwing might be more flexible. Maybe Nightwing wants to take a new direction in fighting crime that Batman doesn't approve of, leading to a conflict.
One possible reason could be Sirius believing he can protect Harry better on his own. Maybe he thinks the Dursleys are too dangerous for Harry and that the wizarding world isn't doing enough. So, he decides to take matters into his own hands and kidnap Harry to keep him safe.
One possible reason could be that Harry is feeling extremely overwhelmed with the challenges he faces in the wizarding world. Sirius is like a father figure to him, so in front of Sirius, he can let out all the pent - up emotions. Maybe he's had a tough encounter with Voldemort or his Death Eaters, and the fear and stress finally break him when he's with Sirius.
Well, in some fanfictions, Sirius might abandon Fem Harry because he has some sort of secret mission that he believes is more important than staying with her. Maybe he discovers some dark prophecy related to Fem Harry and thinks that leaving her will change the course of events. Also, it could be that Sirius has his own inner demons, like guilt from his past, and he feels unworthy of being around Fem Harry so he leaves.
One reason could be that they might have different interpretations of Harry's character in the fanfiction. Hermione, being logical, may see Harry in a more practical light, while Ron, with his emotional side, could have a different view.
Perhaps the wizarding government or authorities were being unjust. For example, if they wrongly accused Harry of a crime he didn't commit, his sense of justice would be outraged. His anger would drive him to fight back and prove his innocence. He's not the type to let false accusations stand.
A simple reason could be miscommunication. Maybe a letter from Harry got lost, or there was a misunderstanding in a conversation, and Sirius thought Harry didn't want to be around him anymore so he starts to ignore Harry in return.
One possible reason could be that he feels unsafe at Hogwarts. Maybe there are threats from dark wizards within the school that the teachers are unable to fully protect him from. Sirius, being his godfather, represents a safe haven.