At first, it might strain their friendship. Harry could feel hurt and misunderstood, leading to some distance between them. He might avoid Hermione for a while, not wanting to face her anger.
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.
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.
Maybe she's yelling at Ron. Their relationship in fanfictions can be quite complex. If Ron says something insensitive or does something stupid, like forgetting an important task that could put their mission in jeopardy, Hermione would surely yell at him.
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.
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.
Mrs Black could be so offended that she starts to plot against Hermione. For example, she might try to get Hermione into trouble with the Hogwarts authorities by spreading false rumors about her.
Perhaps it's related to Harry's association with his father, James Potter. Snape had a long - standing grudge against James, and seeing Harry might bring back those bitter memories. So, whenever Harry does something that reminds Snape of James, like being overly confident or a bit of a troublemaker, he yells at him.
In a fanfic, it could be a scenario where Tonks has been secretly admiring Harry for his bravery. One day, Harry accomplishes something really great and Tonks, overjoyed, yells'mine' in a sense of pride, like he's part of her group of heroic people she admires, and hugs him tightly. For example, when Harry manages to defeat a powerful dark wizard on his own.
She might be shocked at first. Since Harry is yelling, which is out of character for him in many cases, Lily could be taken aback and not know how to respond immediately.