A possible reason could be jealousy. Maybe Hermione becomes jealous of Harry's fame and the attention he always gets. She might feel overshadowed and decide to break away from him to find her own identity outside of his shadow.
Well, there might be a fanfic where Hermione breaks Harry's heart due to her falling in love with someone else in the wizarding world. It could be a character we least expect, like a foreign wizard who visits Hogwarts. This would completely shatter Harry as he has always counted on Hermione's loyalty and friendship. In some fanfics, Hermione's family issues might also play a role. If her Muggle parents were in danger because of Harry's actions, she could break off their friendship in anger.
One possible reason could be their different career paths. Harry might be more focused on Auror work which is dangerous, and Hermione, being the practical person she is, may not want to live in constant fear for his safety. Another reason could be a growing apart in their values. Maybe as they get older, Hermione realizes that Harry has a more impulsive nature when it comes to making decisions regarding the wizarding world's politics, while she prefers a more calculated approach.
Some 'Hermione breaks Harry' fanfics exist because it offers a new and different take on their relationship. The traditional view of their friendship is so strong that exploring a break in it creates a lot of drama and emotional tension, which is interesting for readers.
Harry might be initially shocked and angry. After all, his wand is an important part of his identity as a wizard. He could lash out at Hermione immediately, demanding an explanation for her actions.
Well, one possibility could be that it was an accident. Maybe Hermione was in a rush during a spell - casting practice session and accidentally knocked Harry's wand out of his hand and it broke on a hard surface. Another could be that she was under the influence of some dark magic or a spell that made her lose control and break it in a fit of rage or confusion.
There's also 'Fractured Bonds' which is quite interesting. In this fanfiction, the break - up is caused by a misunderstanding that gets blown out of proportion. It shows how pride and miscommunication can lead to the end of a relationship. Hermione is heartbroken and Harry realizes his mistake too late. It's a really engaging read if you like exploring complex relationship dynamics.
Obviously, Harry would be one of the main characters. He is the one making the decision to break the alliance, so his character development would be central to the story.
One common theme could be power struggle. Since Voldemort is all about power and Harry is his main obstacle, when Voldemort 'breaks' Harry, it shows a shift in the power dynamic.