In some fanfiction, the imprint might be used as a plot device to create jealousy. If Bella still has some feelings for Jacob, seeing him so devoted to someone else through the imprint can make her angry and hateful. Additionally, if the imprint is seen as a way to break up the Bella - Jacob relationship (even if it was a complicated friendship - love relationship), Bella would naturally hate it. For instance, if there are rumors or misunderstandings about the imprint that make it seem like Jacob is completely over Bella, she will resent it.
One possible scenario is when the imprint causes Jacob to be very protective of the person he imprints on. Bella might see this as Jacob neglecting their previous friendship or bond. Another scenario could be that the person Jacob imprints on has a negative attitude towards Bella, and Jacob seems to side with the imprinted one, making Bella hate the whole situation.
Perhaps in the fanfiction, the imprint makes Jacob change his behavior completely. He starts to focus all his energy on the imprinted person, ignoring Bella's needs or feelings. For example, if they were in a dangerous situation together before and Jacob always put Bella first, but after the imprint, he puts the imprinted person first. This sudden change can make Bella hate the imprint. Also, if the imprinted relationship is flaunted in front of Bella, it can lead to her hatred.
One possible scenario is that Jacob reveals a secret that Bella doesn't like. This could make her feel betrayed and start to hate him.
Another scenario could be that Bella does something that endangers Jacob's family or the werewolf pack. This would make Jacob see her as a liability and develop hatred towards her. In some fanfictions, she might accidentally expose the werewolves to their enemies because of her association with the vampires.
One scenario could be that Edward accidentally endangers Bella's family in the fanfiction. Since Bella is very protective of her family, this could be a major turning point for her feelings towards him. For instance, if his vampire nature attracts some dangerous vampires to Forks and they target her family.
It could also be that Jacob has his own ideals and values when it comes to love. He has this image of being with Bella in his mind, and the imprint doesn't fit into that. He might feel that his feelings for Bella are pure and true, while the imprint seems like a more primal or instinctual thing that he doesn't want to succumb to. So, in order to stay true to his own sense of self and his feelings for Bella, he rejects the imprint.
In many fanfictions, Bella's jealousy of Jacob's imprint can be a complex and interesting plot point. It could be because she feels left out or that Jacob has a new, strong connection. Maybe she was used to being the center of Jacob's attention and now with the imprint, she feels like she's losing her place in his life.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions, and you can easily search for 'bella jacob imprint' to find relevant stories.
In fanfiction, Bella could hate Jacob's imprint because it represents a change that she doesn't want to accept. She might have been used to Jacob having a certain kind of love for her, and the imprint is like a sudden shift. It might also be related to the fact that the imprint might lead Jacob to be involved with someone else in a very intense way, and Bella, who has her own complex feelings for Jacob, doesn't like this new development.
Bella's jealousy might be due to envy. She sees Jacob having this intense, almost fated connection with someone else through the imprint. It makes her wonder if she could ever have such a connection with anyone. Maybe she wishes she was the one he imprinted on.
Archive of Our Own (AO3) is also a great place to look for 'bella x jacob imprint fanfiction'. There are many talented authors who post their works there, and you can easily search for the specific type of fanfiction you want using the search bar.
Well, Bella represents everything that Jacob has desired for a long time. Her presence constantly reminds Jacob of what he wants in a relationship. The imprint is something new and different that he doesn't want to accept as long as Bella is in his life. He may think that if he gives in to the imprint, he will lose his chance with Bella forever. And since Bella is constantly there, her influence on him is strong enough to make him reject the imprint.