In some fanfictions, Snape may leave Hogwarts to join a group of wizards or witches with a different ideology. Perhaps he discovers a new magical society that he believes can help him better understand magic or fight against the rising dark forces in a more effective way than he can at Hogwarts.
One possible reason could be that he feels he has fulfilled his purpose there. Maybe he has achieved certain goals related to protecting Harry Potter secretly, and he decides it's time to move on to other things. For example, in some fanfictions, he might leave to explore his own family history or to further his research on the Dark Arts in a more secluded place.
In fanfiction, one reason could be his desire for a fresh start away from the memories at Hogwarts. Maybe he feels he has done all he can there and wants to explore new magical knowledge elsewhere.
Maybe he leaves because of a conflict with the Hogwarts staff. If the new headmaster or some teachers start implementing rules that Harry believes are wrong or unfair, like restrictions on defensive magic classes, he might decide to leave in protest.
One possible reason could be that he feels constantly in danger at Hogwarts. With all the dark magic threats and attacks that keep happening, he might think leaving would keep his friends and himself safer. For example, after the Chamber of Secrets incident, he might have considered leaving to protect others from Voldemort's influence.
One reason could be to search for a powerful magical artifact outside of Hogwarts that they believe is crucial for defeating a new dark threat. In fanfiction, they might feel that Hogwarts has become too dangerous or restricted in terms of resources for their mission.
In fanfiction, Snape might punish Draco for getting involved with the wrong crowd. For example, if Draco starts to associate with Death Eaters - in - training or those with malicious intentions. Also, if Draco fails to complete his academic tasks or cheats in exams, Snape would surely take action. This is because Snape values knowledge and academic integrity in Hogwarts. Additionally, if Draco causes trouble during important school events or ceremonies, Snape would likely punish him to set an example for other students.
One possible reason could be peer pressure. Maybe the other Slytherins in the fanfiction are pressuring him to cheat in order to maintain the house's reputation for being cunning and getting ahead at all costs. Another reason might be his own insecurities. He could feel that he's not smart enough or good enough compared to his classmates, so he resorts to cheating as a way to seem more competent.
One possible reason could be a dark turn in the story. Maybe Harry is under the influence of a dark magic or a powerful and evil entity that makes him lose control and start to destroy Hogwarts. For example, if he was possessed by a powerful dark spirit that wanted to eradicate the symbol of the wizarding world's good, which is Hogwarts.
It could also be that Snape represents everything that Harry hates about Hogwarts at that moment in the fanfiction. Snape's strictness, his partiality towards certain students, and his general unfriendly attitude might make Harry feel that Hogwarts is no longer the safe haven it once was. So, he leaves, thinking that he can find a better place where he doesn't have to deal with Snape's negative presence.
In some fanfictions, it might be because Snape exposed a secret of Harry's that led to his departure.
A plotline might involve Snape being removed unjustly. His allies or some students who knew his true nature might try to fight for his reinstatement. There could also be a story where Snape's removal causes a power vacuum in Hogwarts, and different factions start vying for control of certain aspects of the school. It could also lead to a discovery of secrets that Snape was protecting while he was at Hogwarts.