The fight could start because of a competition at Hogwarts. For example, if there was a magical duel competition, and both James and Snape entered. They might be pitted against each other in a match. Their existing animosity would make the duel more intense, and it could easily spill over into a full - fledged fight outside of the competition rules. James' bravado and Snape's determination not to be bested would fuel the conflict.
In fanfiction, their fight could be triggered by a misunderstanding. Maybe Snape was working on a project in the Potions dungeon, and James thought he was up to something sinister. James, being the impulsive type, jumps to conclusions and attacks Snape. Or it could be that Snape overhears James talking badly about him to his friends and decides to confront him, which quickly turns into a fight.
One reason could be jealousy. Snape might be jealous of James' popularity and charm. James, on the other hand, could be jealous of Snape's close friendship with Lily in their early years. Another reason is their different personalities. James was outgoing and bold, while Snape was more introverted and brooding. Lily might be attracted to different aspects of each of them, which could lead to the fight as they both compete for her attention.
A fanfiction of their fight could be really intense. James could be motivated by his jealousy towards Snape's closeness with Lily. He might want to show off in front of her. Snape, who has a deep - seated dislike for James due to his bullying, would be more than ready to engage. Their fight could range all over the Hogwarts grounds, from the corridors to the Forbidden Forest. Spells would be flying everywhere, and other students might get caught in the crossfire. It would be a chaotic and exciting scenario to read about.
Perhaps Snape believes that James has some crucial information that he needs and he thinks torture is the quickest way to get it. Or maybe there's a power struggle going on. Snape wants to assert his dominance over James, who might be seen as a rival in some way, either for a position at Hogwarts or in the wizarding community. Also, it could be due to a misunderstanding that has spiraled out of control, leading Snape to think that James is a greater threat than he actually is.
In some fanfictions, it could be related to Lily. If James did something that Snape perceived as a threat to his relationship with Lily, even if it was just being overly affectionate with her in front of Snape, Snape might lash out at James. Snape had deep feelings for Lily, and any sign of James getting in the way could trigger an attack.
Differing ideologies during the wizarding war. If James was seen as a threat to Snape's side (even if Snape was on the wrong side, from a moral perspective), Snape could justify killing him. For example, if James was too aggressive in fighting the Death Eaters and Snape thought it would lead to more bloodshed, he might take matters into his own hands to stop James.
One possible theme could be redemption. Maybe James realizes the wrongs he did to Snape and the kiss is a sign of his attempt to make amends. Another theme could be a change in their relationship dynamics, from enemies to something more complex. For example, a sudden realization of a deeper connection.
Lily. Since Snape and Lily were friends when they were young, and James had a crush on Lily. Snape might have had a special connection with Lily that James desired, so he could be jealous. Also, Snape was always kind of an enigma, and that mystery around him might have made James jealous as well. He might have thought Snape had some sort of power or charm that he didn't.
In this type of fanfiction, a plot twist could be that Snape saves them, but they end up having to go into hiding in a completely unexpected place. Maybe they have to live among muggles in a way they never thought possible. Another plot twist could be that Snape saves them, but then realizes that he has put himself in a very dangerous position with Voldemort's followers. So he has to find a way to protect himself while also protecting Lily and James. And there could also be a plot twist where Snape saves them, but they don't believe his motives are pure and they try to escape from him, leading to a whole new set of adventures and challenges.
Snape's view of James might not change much at first. He has such deep - seated hatred for James due to their past. But if the fanfiction shows James in a more positive or sympathetic light, he may start to question his long - held beliefs about him, just a little bit.
Perhaps in the fanfiction, James is seen as more accepting of Lily's friends and her social circle. Snape, on the other hand, might be associated with a darker crowd or have some beliefs that Lily doesn't agree with. For example, if Snape is too involved with the Dark Arts in the fanfiction, it could be a turn - off for Lily.