One plot idea could be that Hermione gets angry at Snape for unfairly deducting points from Gryffindor. She confronts him in his office and they end up having a heated debate about fairness in the Hogwarts system. Another could be that Snape discovers Hermione is working on a dangerous magic experiment without proper authorization and she gets angry when he tries to stop her. A third idea is that Hermione overhears Snape making some snide remarks about her Muggle - born status and she angrily challenges his old - fashioned views.
At first, Hermione's anger towards Snape might be based on his general surliness and what she perceives as his unfair treatment of students. But as time goes on, if they are involved in a dangerous situation in Hogwarts, for example, a dark magic threat. They might find that they need to rely on each other's skills. Snape's expertise in potions and dark arts, and Hermione's vast knowledge and quick thinking. This could gradually thaw their relationship. Also, if Snape were to open up a bit about his past, it could make Hermione more sympathetic towards him, and they could develop a more complex relationship that is no longer just based on anger.
The 'time - travel' trope is also quite common. For example, Hermione might go back in time and interact with a younger Snape, which can lead to all sorts of new storylines and character developments.
One great Snape and Hermione fanfiction is 'The Unbreakable Bond'. In this story, Hermione discovers a hidden side of Snape during her research in the Hogwarts library. Their relationship starts as a mentorship but gradually evolves into a deep friendship that defies the expectations of the wizarding world. It beautifully portrays their individual characters and how they can complement each other.
Hermione might become more guarded at first. She is used to being independent and suddenly being 'gifted' to Snape is a big change. But over time, she could learn to be more patient and understanding. Snape, on the other hand, might soften a bit. His usual cold exterior could crack as he gets to know Hermione better.
Another reason could be related to school work. If there are new rules in Hogwarts that she deems unfair regarding academics, like restrictions on library access or new grading systems that don't reward hard work properly. Hermione is all about learning and fairness in education, so this could really make her angry.
In some fanfictions, Harry might be angry with Ron and Hermione if he feels they are keeping secrets from him. For example, if they discover something important about Voldemort's plans but don't share it right away, Harry could get angry. He's used to relying on them and when that trust is broken, even if it's a misunderstanding, his anger can flare up.
It's hard to say who would be the clear winner. Hermione is intelligent and quick - witted, but Snape has years of experience and a great deal of magical knowledge. If it's a battle of words, Hermione might hold her own for a while, but Snape could use his authority to shut her down.
She might give him cold stares in class. Hermione is not one to shy away from showing her emotions through her expressions. So, every time Snape is in her line of sight, she could fix him with a withering glare that clearly shows her displeasure.
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.