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.
One possibility is that Charlie is shocked and immediately starts asking a lot of questions. He might be worried about his daughter being alone with Edward. For example, he could demand to know what their relationship really is.
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.
In some plotlines, it could be that Bella has made a deal with Peter in order to escape Edward's over - possessive nature. Peter might have his own reasons for wanting to get involved, like a long - standing feud with Edward's family. So, he uses his wits and resources to whisk Bella away to a place where Edward can't find her. This could lead to a whole new adventure for Bella as she adjusts to life away from Edward and with Peter's protection.
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.
There are several possible reasons. Firstly, a sense of being controlled. If Edward is constantly making decisions for her or restricting her actions, Bella would want to break free. Secondly, self - preservation. If she realizes that the relationship is putting her in more danger than she can handle, she'll run. Thirdly, a change in her feelings. Maybe she falls out of love with Edward or realizes she was never truly in love, but rather in some sort of infatuation. So, she runs away to sort out her emotions and her life.
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.