Perhaps he sees in the fanfiction a sense of creativity and passion from the fans. The way they build on the world J.K. Rowling created, adding new plotlines and character arcs, might appeal to his own love for the magical world and its many secrets. He may also enjoy seeing how the fans fill in the gaps that the original books left.
It could be that in the fanfiction, some of the relationships are developed in a way that he finds interesting. For example, the relationship between him and Harry might be reimagined in a more positive or complex light, which makes him see new possibilities and thus like it.
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.
Maybe Harry Potter is tired of the unrealistic portrayals of Snape in fanfiction. Often fanfictions can exaggerate characters' traits, and Harry, who knew Snape in real life, might find these interpretations too far - fetched.
One possible reason could be that fanfiction often takes creative liberties that may distort the complex character of Snape that J.K. Rowling created. Snape has a very intricate backstory and personality in the original series, and fanfiction might simplify or misinterpret it.
One reason could be that Harry is under an extreme amount of stress. He has so many burdens on his shoulders in the wizarding world, like fighting Voldemort. This stress could manifest physically as a seizure, especially if he is in a tense situation in front of Snape, who is often a source of anxiety for him. For example, if Snape is about to accuse him of something he didn't do while he is already worried about other threats to the wizarding world.
Perhaps Harry has a hunch that Snape is involved in some secret project or fight against the dark forces that requires basilisk parts. Harry, being the hero he is, decides to provide Snape with the parts to aid in this unspoken cause. It could also be a sign of Harry's growing maturity and his ability to see beyond their past differences.
Perhaps in this fanfiction, Snape shows a side of himself that is completely different from what Harry has known. He might be more open and honest with Harry, sharing secrets that make Harry believe he can be trusted. Like Snape might disclose some long - held information about Harry's parents that only he knew, which makes Harry think Snape has been on his side all along.
Well, if such a fanfiction exists, one possible reason could be a huge misunderstanding. Maybe Harry discovers something about Snape that he misinterprets and then hounds Snape with accusations and guilt - tripping until Snape can't take it anymore. Another reason could be if dark magic is involved in some way, like Harry is under the influence of a dark spell that makes him act out of character and target Snape relentlessly.
It could be that in the context of the fanfiction, Snape believes Harry has been disrespectful towards him or other teachers. For example, if Harry were to talk back or show disobedience in class, Snape would likely punish him as a way to assert his authority.
One reason could be that he realizes Harry has a lot of potential and wants to nurture it. He sees that Harry is in a difficult position, being the target of Voldemort, and decides to help him despite their past differences.
One reason could be that the creators of such fanfiction are die - hard Snape fans. They might feel that Snape is the most interesting and underappreciated character in the 'Harry Potter' series. So, they create fanfiction where Harry Potter, who they may see as getting too much attention in the original, is not as great, to put more focus on Snape.