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.
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 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.
One possible reason could be Snape's unfair treatment of Gryffindor students. Hermione, being a strong advocate for justice, might not tolerate his constant jabs at her house. For example, in the original story, Snape often took points from Gryffindor without what Hermione might consider proper cause. In fanfiction, this could be exaggerated, leading to her blowing up at him.
It could completely transform their relationship. Initially, they had a rather strained relationship due to Snape's often harsh demeanor and Hermione being a Gryffindor. But once he confides in her, she may feel a sense of responsibility towards him. This could lead to her defending him in certain situations. Snape might also open up more about his past and his reasons for his actions, which would make Hermione more empathetic towards him.
Well, one reason could be that he sees her intelligence and thirst for knowledge, which he respects. He might feel a sort of kinship as he was also a very intelligent student himself when he was younger.
Maybe Snape made a snide comment about Hermione's intelligence or her Muggle - born status. Snape has a rather acerbic tongue, and if he said something derogatory about Hermione's abilities or her heritage, she would surely be furious. After all, Hermione works extremely hard to prove herself in the wizarding world and any attack on her intelligence or background would be a big blow.
One possible reason could be the stress from her studies. Hermione is always under a great deal of pressure to excel academically. Maybe she reached a breaking point due to the overwhelming workload. Another reason might be some kind of conflict with her friends. For example, if she had a big fight with Harry or Ron over something serious, it could leave her feeling broken.
One possible reason could be a powerful spell gone wrong. Maybe she was caught in the crossfire of a dark magic spell that Snape was either trying to counter or was involved in accidentally. Another reason might be extreme emotional shock. For instance, if she discovered some dark secret about Snape that was so overwhelming it sent her into a catatonic state.
One possible reason could be that Snape sees Hermione's value as a brilliant student. He might recognize her potential and not want it to be wasted just because of her dad's actions or situation. Maybe he has a sense of justice deep down, despite his often cold exterior.
One possible reason could be that Snape has shown unexpected kindness to Hermione in the fanfiction. Maybe he has protected her from some danger secretly, which makes her feel she can rely on him and thus feel safe.