It could also be that the author wanted to show her vulnerability. Hermione is often seen as a very strong and capable character. By having her in such an embarrassing situation, it adds a new dimension to her character. It could be a way for the writer to explore how she deals with humiliation and how her friends, like Harry and Ron, react to this unexpected side of her.
It could potentially make her seem more human. In the original series, Hermione is often portrayed as nearly perfect. This kind of incident in a fanfic would show that she is not immune to embarrassing situations, making her more relatable to readers.
One possible reason could be a miscommunication. Maybe Hermione accidentally reveals a secret of Harry's that he didn't want known, and this causes him to feel betrayed and start to hate her. Another reason could be jealousy. If Hermione gets more attention or praise for her magical abilities than Harry in the fanfic, he might develop feelings of envy and hatred. Or perhaps there's a love triangle situation where Hermione is involved with someone Harry doesn't like, and that causes his hatred.
One possible reason is that the fanfic writer wants to create conflict. By making Hermione not believe Harry, it adds tension to the story.
In fanfics, the relationships between characters can be explored in new ways. If the fanfic writer decides to show a rift between Hermione and Harry for the sake of drama, they might create situations where Hermione doesn't believe Harry. This could be due to a series of miscommunications or actions that Harry takes which seem out of character to Hermione.
In some fanfictions, it might be due to a broken relationship. For example, if something goes terribly wrong between her and Ron or Harry, she could sink into a deep depression and see no way out. She may feel that she has lost the most important people in her life and can't bear the emotional pain.
Maybe in this fanfiction she experiences a great loss, like the death of a loved one in a very tragic way. For example, if Ron or Harry were killed in a battle and she blamed herself for not being able to prevent it. This overwhelming guilt could be a reason for her to try to kill herself.
It could be that they lied to Harry about something really significant. In the wizarding world, trust is built on truth - telling. If they told a big lie, like about the true nature of a magical object that was putting Harry in danger, he would be very angry. And if their actions led to the death of someone Harry cared about. For instance, if they made a wrong move during a fight that caused an ally to die, Harry would find it very hard to forgive them.
One possible reason could be that Hermione has a different romantic vision. In the original series, she might see Harry more as a friend. In the fanfic, her character could be written as being focused on her own personal growth and goals, which don't align with a romantic relationship with Harry.
One reason could be the strict control by the official copyright holders. They might be worried about fanfic diluting the official brand or misinterpreting the original story. Another factor could be some fans' purist view. They only want to stick to the original works by J.K. Rowling and consider fanfic as something not in line with the 'true' Harry Potter universe.
One possible reason could be that they are wrongly accused of a serious crime within the wizarding world. Maybe some dark magic items are found in their possession and the authorities suspect them of being involved with dark wizards, without fully investigating the real source of those items.