Perhaps in an academic competition within Hogwarts. Snape could be the judge and Hermione, overconfident in her knowledge, makes a mistake that Snape points out harshly, which could be seen as 'beating' her in a sense. But then Hermione learns from her mistake and comes back stronger, impressing Snape with her ability to grow. This would be a plot that focuses on growth and learning rather than something negative.
It could be that Snape and Hermione are on opposite sides of a school - wide mystery or challenge. Snape, using his experience and cunning, solves the mystery first and in the process, makes Hermione realize that she still has a lot to learn. This 'beating' is more about him being one step ahead in this particular situation, but it also leads to Hermione respecting Snape more and vice - versa, opening up new possibilities for their relationship in the fanfiction.
One possible theme could be redemption. Maybe Ron realizes his wrongdoings and tries to make amends. As for Snape, he could be a figure of guidance or an observer in the situation. Another theme might be misunderstanding. The so - called 'abuse' could start from a huge misunderstanding between Ron and Hermione, and Snape could be involved in a way that helps clear things up.
One possible plotline could be a time - travel or alternate - reality scenario. For example, in an alternate universe where the relationships between characters are different, Snape and Hermione could have a relationship that leads to her getting pregnant. The story could then focus on how they deal with the consequences in that different world, perhaps facing opposition from others due to their age or social differences within the wizarding community.
Perhaps Snape discovers Hermione's extraordinary intelligence in a new way, which makes him excited. Maybe she solves a really difficult magical problem that he thought was unsolvable, and this newfound respect and admiration leads to his excitement.
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 plot could be that they have a deep conversation about their past differences and how they overcame them. They might share their hopes and fears for the future. Maybe they start with a quiet dinner in their new home, just enjoying each other's company and reminiscing about how they fell in love despite all odds.
One interpretation could be that Snape wants to taste a potion Hermione has made. In the wizarding world, potions are a big part of magic, and Snape is known for his expertise in potions. So, if Hermione creates a new and innovative potion, Snape might be eager to taste it to evaluate its quality and effects.
One possible reason is Snape's prejudice. He might have some sort of bias against Gryffindors in general, and Hermione, being a very Gryffindor - like student, gets the brunt of it. He may expect her to make mistakes typical of Gryffindors like being overly bold without thinking. Another factor could be that Hermione is so intelligent and inquisitive that Snape feels threatened. He likes to be in control of the knowledge in his classroom, and Hermione's constant questions and thirst for knowledge might make him act tough towards her.
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.
Well, one possibility is that she gets frustrated with the slow progress of the 'good side'. Maybe she sees all the bureaucracy and inefficiency in the fight against the dark forces and decides that the dark side can offer a more direct way to achieve her goals, like a more efficient magical society. But this would be a huge shift from her original character.
One possible plot development could be that Snape's claim over Hermione creates a great deal of conflict within the wizarding world. The Order of the Phoenix might see it as a threat or a strange alliance. Hermione herself could initially resist but then start to understand Snape's motives, which could be related to protecting her from a greater danger.