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.
Well, it could be simply because of the bad blood between them. Snape has been tormenting Harry since his first day at Hogwarts. He constantly deducts points from Gryffindor for the smallest of reasons when it comes to Harry and his friends. This continuous harassment could make Harry believe that Snape is not a good influence in the school. Also, Harry might think that Snape is not teaching Potions effectively. We know that Snape is brilliant at Potions, but his teaching style might not be conducive to the students' learning. He may be too strict and not allow enough creativity or exploration in the subject, which could lead Harry to want him out of the teaching position.
Maybe Harry wants Snape fired because of Snape's past associations. Harry discovers that Snape was once a Death Eater. Even though Dumbledore vouches for Snape's change of heart, Harry might still be suspicious. He could fear that Snape might relapse or that his past could endanger the students. In addition, Snape's role in the Triwizard Tournament mystery, where he seemed to be involved in some shady business, could also fuel Harry's desire to have him removed from Hogwarts. Harry is always looking out for the safety of his friends and the school as a whole, and Snape's actions make him seem like a liability.
Well, perhaps it was because of a conflict with a powerful figure. Maybe she had a huge argument with the Headmaster or someone from the Board of Governors. If she strongly opposed a decision that the higher - ups were very much in favor of, it could lead to her dismissal. For instance, if there was a plan to cut down on certain magical subjects that she thought were essential for students' education. And in a fanfic world, there could be some made - up reasons too, like a mysterious prophecy that said her presence at Hogwarts would bring some great danger, so they fired her to avoid it.
Perhaps Harry witnesses Snape being extremely unfair to a group of students, like constantly giving them detention for no good reason. Harry decides to take a stand and gathers statements from the students. He then goes to the Hogwarts board of governors and presents his case, leading to Snape's dismissal.
In some fanfictions, it might be due to political reasons within Hogwarts. For example, if there is a power struggle between different factions, Snape could be seen as a threat or a liability to one side and they find a way to get him fired. His loyalty has always been somewhat in question in the eyes of some, so it could be exploited.
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.
Well, some writers might create such fanfics to add a new layer of drama. The relationship between Harry and Snape was already full of conflict in the original story. By making Harry the abuser, it amps up the intensity and gives a new angle to their interactions. Also, it could be a way to explore the consequences of extreme emotions like hatred in a different context. In the original, Harry didn't really cross the line into abuse, but in these fanfics, writers can show what would happen if he did.
Perhaps in fanfic Harry complains about Snape due to Snape's relationship with his father, James. Snape clearly had a lot of animosity towards James, and sometimes that spilled over onto Harry. Harry might feel that Snape is holding a grudge against him for something his father did, which is unfair, and thus complain.
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 the complex relationship between them. Snape's mixed feelings of resentment and a strange sense of protectiveness towards Harry in the original series can be explored more deeply in fanfiction through fantasies. Another reason might be the popularity of both characters. Fans want to see different interactions between them that were not fully shown in the books.
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 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.