One possible reason could be Snape's unfair treatment of Gryffindor students. Hermione, being a strong advocate for justice, might not tolerate his constant bias against her house. She could yell at him when he unjustly deducts points from Gryffindor for minor reasons.
One possible reason could be that Harry did something reckless without consulting Hermione. For example, if he went off on his own to face a dark wizard, Hermione, being the cautious and logical one, would be furious. She values planning and teamwork, and Harry's solo actions might seem to her as endangering himself and others needlessly.
Snape might initially be taken aback. He's used to students being intimidated by him, so Hermione's outburst could shock him into momentary silence. Then he might retaliate with his usual sarcasm, trying to put her in her place.
In a fanfiction, it could be that Ginny is being too reckless. Hermione, being the more cautious one, is always worried about getting into trouble. If Ginny is constantly sneaking out or getting involved in dangerous adventures, Hermione might yell at her to stop putting herself and others at risk.
It could also be because of Naruto's own insecurities. He might be afraid that Hinata's actions are drawing too much unwanted attention or putting herself in harm's way, and he yells to try and protect her in his own, brash way. He doesn't want to lose her, but doesn't know how to express it other than through yelling.
One possible reason could be Snape's unfair treatment of Gryffindor students in the fanfiction. Hermione, being a strong advocate for justice and fairness, might not be able to tolerate his constant bias against her house. For example, if Snape gives Gryffindor students harsher punishments than students from other houses for the same infractions, Hermione would likely be furious and yell at him.
One possible reason could be a misunderstanding. Maybe Hermione thought Snape was involved in some dark plot against her friends. In the wizarding world, there are often secrets and deceptions, and if she got some false information, it could lead her to take such drastic action.
Harry might become more determined to prove Snape wrong. He's a stubborn character, and Snape's yelling could fuel his desire to show that he's not the misbehaving student Snape seems to think he is.
One reason could be differences in teaching methods. Hermione is a very studious and by - the - book student, and Snape has his own rather unorthodox and often harsh teaching ways. For example, in the official books, Snape is known for his sarcastic remarks towards students, and Hermione might not tolerate this in a fanfiction scenario. She could argue with him about how his teaching is not conducive to a positive learning environment.
One reason could be Hermione's intelligence. Snape might recognize that she is smart enough to understand his complex situation. He could see her as someone who could offer a different perspective on his problems.
Perhaps Snape was being overly harsh with one of Hermione's friends. She is very protective of Harry and Ron. If Snape said something mean or did something to harm them, Hermione would surely stand up and yell at him. For example, if he gave Ron a particularly difficult detention for no real fault of his own.