In some fanfictions, James might be possessive of Hermione due to a prophecy or some sort of pre - ordained connection. It could be that he believes she is the key to something important in his life, like saving the wizarding world, and so he becomes possessive to ensure she is on his side. Another reason could be that he has had a past experience of loss, and Hermione represents something he doesn't want to lose again, so his possessiveness is a form of self - protection.
Maybe it's because Hermione has unique qualities. Her intelligence and strength might attract James, and his possessiveness could stem from a fear of losing someone so special.
In fanfiction, Tom Riddle may be possessive of Hermione because she represents something he can't fully understand or control. Her moral compass is so different from his. He may think that by possessing her, he can gain some of that goodness or use it to his advantage. Also, Hermione's popularity and influence among her peers might make Riddle want to have her as a trophy of sorts, to show his superiority over others in the wizarding world.
One reason could be that Fenrir sees Hermione as a unique and powerful individual. Her intelligence and magic might attract him in a way that makes him want to possess her, as if she's a prized possession that no one else can have.
Love could be the main reason. Since he loves Annabeth deeply, he doesn't want to lose her, so he becomes possessive.
Well, one reason could be that she discovers some long - lost family inheritance. Maybe her family had a hidden vault full of gold and magical artifacts that she stumbles upon. It's a common trope in fanfiction to give characters unexpected inheritances.
One reason could be that Minerva sees Hermione as a kindred spirit. Hermione is highly intelligent and dedicated to her studies, just like Minerva was when she was younger. So, Minerva is possessive because she wants to nurture that part of Hermione and sees herself in her. It's like she wants to relive her own glory days through Hermione.
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.
Protectiveness. Sasuke has seen a lot of danger in his life. He knows Sakura is a valuable person, both as a friend and as someone he cares about. So his possessiveness could stem from his desire to keep her out of harm's way. He doesn't want any bad guys to get near her.
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 reason could be for the sake of novelty. Fanfic writers like to create unique and unexpected scenarios, and this is a very different take on the Potter family. It grabs readers' attention.
One reason could be the author's desire to rewrite the relationships in a more edgy way. They might think that making Hermione mean to Harry will attract more readers who like drama.