Well, it changes their relationship a great deal. Usually, in the original story, Snape and Harry have a very antagonistic relationship. But in fanfictions where Snape raises Harry, they start to understand each other better. Snape sees Harry as more than just James Potter's son, and Harry realizes that Snape has his own reasons for his actions.
In these fanfictions, Snape raising Harry means that Snape becomes a mentor figure to Harry. He imparts his knowledge of magic, especially in areas like potions and the Dark Arts (for defense purposes). This changes their relationship from one of hatred to one of mutual respect. Harry starts to trust Snape, and Snape becomes more protective of Harry. Their relationship evolves into something like a father - son relationship in some cases, with all the complexity and love - hate that comes with it.
Well, it would completely turn the story on its head. In the original, Snape is an adult figure and often at odds with Harry. But if Harry were to raise Snape, perhaps Snape would grow up with a different view of Harry. He might not be so bitter and resentful. Harry could instill in him values that would make Snape less likely to be drawn to the Dark Arts. This would also mean that the whole Hogwarts dynamic would change. Snape might be a much more positive influence on the students instead of the intimidating figure he was in the original story.
In the fanfiction, Snape's impression might make him more protective of Harry. He could start to subtly look out for Harry's well - being, whether it's in the face of other students' bullying or more dangerous threats from the dark side. This would be a significant change from their usually strained relationship in the original story.
On the other hand, it could also lead to a strange kind of understanding. Maybe Harry realizes that Snape is under a great deal of pressure and that the punch was a momentary lapse. This could make Harry more empathetic towards Snape, although he might still be angry about being punched.
It changes their relationship drastically. Initially, they were at odds. But with Snape taking Harry in, they start to see each other in a new light. Harry might see Snape's more vulnerable side and Snape might see Harry as more than just James Potter's son.
One possible fanfiction could be about Snape taking Hermione under his wing after realizing her extraordinary intelligence and potential. He might secretly tutor her in advanced potions and dark arts defense, leading to a unique bond between them. This could also cause some conflict with other Hogwarts staff and students, as Snape has a rather infamous reputation.
One idea could be that Snape takes Harry in secretly. He teaches Harry advanced potions and magic in a more personal way, away from the prying eyes of Hogwarts. Harry begins to see Snape in a new light, not as the mean professor but as a strict yet caring guardian.
Snape becomes more empathetic. He has always been a complex character, but in this scenario, he has to open up his heart to Harry. His cold exterior starts to crack as he sees Harry's vulnerability. For example, he might show small acts of kindness like making sure Harry has enough to eat or a warm place to sleep.
The relationship would become extremely strained. Harry would likely go from having some level of respect or at least tolerance for Snape to feeling intense hatred. He might avoid Snape at all costs and even start to plot revenge in his head.
In a fanfiction scenario, Harry's actions could cause a complete breakdown in any potential for a positive relationship between them. Snape's loyalty to Dumbledore and his role in protecting Harry from the shadows would be put at risk. Harry would have to face the fact that he may have made a huge mistake. And Snape, who has sacrificed so much already, would be in an even more precarious position, both with Voldemort and in the wizarding world in general. This could lead to a chain of events that completely alters the course of the wizarding war, with far - reaching consequences for both Harry and Snape.
The relationship would become more complex. Snape would have a certain level of control over Harry as his familiar. This would force Snape to be more responsible for Harry's well - being. Harry, in turn, would have to rely on Snape in a new way.