In fanfiction, Batman could quit the Justice League because of a personal loss. If someone close to him, like Robin, were killed during a Justice League mission due to a misstep or lack of coordination within the team, he might hold the League responsible. This emotional trauma could drive him away. He may also feel that the League's goals are starting to diverge from his own. He is mainly focused on protecting Gotham and its people, and if the Justice League starts getting involved in more intergalactic or large - scale political matters that don't directly benefit Gotham, he could decide to part ways.
Perhaps he quits due to a betrayal. Maybe one of the members of the Justice League does something that Batman views as a huge betrayal, like leaking his secret identity or using his technology without permission. This could shatter his trust in the team and lead him to leave. Also, it could be because he feels the Justice League is becoming too reliant on certain members or powers. Batman, with his wits and resources, might not want to be part of a group that isn't using their own skills to the fullest and instead depending on superpowers all the time.
One reason could be a moral disagreement. Batman has a very strict moral code. If the Justice League were to engage in actions that he considered too extreme or unethical, he might quit. For example, if they started using excessive force on villains without proper trial. Another reason could be burnout. Constantly fighting crime and dealing with the politics within the Justice League could take a toll on him. He might feel that he needs to step away to regain his sanity and focus on protecting Gotham in his own way.