One possible reason could be that Edward believes Charlie is a threat to Bella in some way that Charlie doesn't realize himself. Maybe Charlie unknowingly gets involved with some dangerous elements, and Edward, with his vampire senses, detects it.
Perhaps there is some supernatural influence on Charlie that Edward notices. It might be a spell or some other force that is making Charlie act in a way that could harm Bella in the long run. So, Edward takes it upon himself to save Bella from this potential danger.
Edward could use his mind - reading ability. He reads Charlie's intentions and plans his moves accordingly. If Charlie is about to make a decision that Edward believes will be bad for Bella, he can intervene at the right time. He might also be able to manipulate the situation subtly so that Charlie changes his mind without realizing it.
In many such fanfictions, Edward might use his superhuman speed to reach Bella just in time. He could have sensed her danger through his vampire instincts and dashed to the cliff edge, grabbing her before she falls.
Bella would likely be very frightened during the car incident. Once Edward saves her, she'd be extremely relieved and probably feel even more attached to him. Edward, on the other hand, would be initially worried and focused on getting Bella to safety. After saving her, he might feel a sense of relief as well, but also a bit of that over - protective feeling that he often has for Bella.
She might be in shock at first. After all, she was in a life - threatening situation. But then she could feel extremely grateful towards Edward and their relationship might grow stronger.
Another reason might be Edward's overprotectiveness. He could have made a decision for Bella without consulting her first, like preventing her from seeing a friend. This kind of controlling behavior could make Bella feel frustrated and end up in tears.
One reason could be a shift in the story's setting. If the fanfiction is set in a different time or place, Bella's values and interests might change, leading her to not like Edward. For instance, if it's a modern - day setting with different social norms, she may find Edward's old - fashioned ways off - putting.
Perhaps she has her own vision of their relationship and doesn't want it to be influenced by the often - strange and varying ideas in fanfiction. Fanfiction can be full of outlandish concepts that she doesn't want to be part of. She wants to preserve the unique and special nature of her relationship with Edward as it is in real life.
One possible reason could be that Bella discovers a different side of Jasper that she finds more appealing. Maybe Jasper shows a deeper understanding of her in some aspects that Edward lacks. For example, Jasper's past experiences might make him more empathetic towards Bella's own struggles in a way that Edward, with his own set of vampire characteristics, doesn't quite get.
One reason could be loyalty. Emmett is part of the Cullen family, and Bella is important to Edward, who is also his family. So, he would do anything to protect her for the sake of family unity. Another reason might be his sense of justice. If he saw Bella in an unfair or life - threatening situation, his nature would drive him to save her.
Another reason could be related to the biology aspect specifically. In the fanfiction, the author may have created a unique lore where there is something in the biology of vampires and humans that makes a bite in a biology class significant. Maybe there are certain chemical reactions that occur only in a scientific environment like a biology class that are essential for the bite to have a particular effect, such as awakening a dormant power within Bella or creating a special bond between them.