Snape could be acting on Dumbledore's orders. Dumbledore might have a grand plan that involves Snape using potions to change Harry in certain ways. It could be part of a strategy to defeat Voldemort in the long run. Snape, being loyal to Dumbledore, would then carry out these actions using his potions expertise.
Maybe Snape wants to train Harry better. By using potions to change Harry's abilities or characteristics, he can expose Harry to different challenges and make him a stronger wizard. For instance, if he gives Harry a potion that temporarily takes away his ability to use magic, Harry will have to learn to rely on other skills.
In some fanfics, Snape may use a potion similar to the Felix Felicis, the luck potion. But instead of just bringing luck, this modified version could be used to change Harry's fate or the course of his actions. It could make Harry more inclined to make certain choices that Snape desires. Also, there could be a potion that can temporarily suppress Harry's magic, which Snape might use to keep Harry out of trouble or to protect him in a different way.
One possible reason could be that in the fanfic, Harry discovers Snape's deeper motives earlier. Maybe he stumbles upon Snape's memories or has a series of interactions that show Snape's true loyalty to Dumbledore and his complex role in protecting Harry all along. This new understanding makes Harry admire Snape.
Maybe he was poisoned. There could be someone who slipped a harmful potion ingredient into his cauldron without him noticing. It's a common plot device in fanfics to create drama.
It could be that he has a bad accident in the potions lab. For example, a potion explodes and nearly kills him or one of his friends. This traumatic experience makes him lose his confidence and interest in potions, leading him to quit as seen in some fanfictions.
One reason could be that he's facing extreme pressure in potions class. Maybe he's constantly compared to others, like Snape always having high expectations of him. Another reason might be that he has some kind of emotional turmoil related to his past traumas while in the potions environment. For example, the smell of a certain potion might remind him of a difficult time at the Dursleys.
One possibility is that a potions accident could cause a time - related mishap. Maybe the potion was supposed to be a simple Sleeping Draught but due to the accident, it creates a time - loop. The characters find themselves repeating the same day over and over until they figure out how to reverse the effects of the botched potion. This could be a really interesting plot device in a Harry Potter fanfic as it would allow for a lot of character development and exploration of different choices within the same day.
One possible reason could be Snape's unfair treatment of Harry and his friends. Snape often showed blatant favoritism towards Slytherin students and was overly harsh on Gryffindors, especially Harry. This constant bias could lead Harry to want him fired. Another reason might be Snape's connection to the Dark Arts. Harry, having faced Voldemort, might be worried about Snape's knowledge and use of dark magic within Hogwarts. Also, Snape's generally unpleasant demeanor towards students could be a factor. His sarcastic remarks and cold attitude might make Harry think that he is not a suitable teacher for Hogwarts students.
One possible reason could be that Harry breaks a major rule in the wizarding world within the fanfic. Snape, being a strict and by - the - book person, grounds him as a form of punishment. For example, if Harry uses dark magic without permission, Snape would surely take strict action.
One possible reason could be copyright infringement. If the fanfiction uses too much of the original 'Harry Potter' material without proper authorization, J.K. Rowling (or those in charge of the franchise) might take legal action. Another reason could be if the fanfiction misrepresents the characters in a way that goes against the intended spirit of the original work.
Perhaps he likes to see how fans re - imagine his character. He might be curious about how others view his actions and motives throughout the story.