As time goes on, Snape might start to open up a bit more to Harry about his past and his reasons for protecting him. This could lead to a more understanding and even a friendship - like relationship between them. For example, Snape could share stories about Harry's mother, which would make Harry feel closer to him.
Well, it could start with Harry realizing that Snape's actions, though often harsh, were sometimes driven by a deeper purpose. Maybe he discovers Snape's past and starts to see him in a new light. This new understanding could gradually turn into an attachment as Harry sees the complexity of Snape's character.
At first, their relationship is likely to be very tense. Harry is used to seeing Snape as an enemy. But as Snape starts to mentor him, Harry begins to see Snape's knowledge and skills. Snape, on the other hand, might start to see Harry as more than just James Potter's son. As time goes on, they develop a mutual respect. Harry respects Snape's magical abilities and Snape respects Harry's determination. Eventually, they could become something like a reluctant teacher - student duo that also has elements of a father - son relationship, especially considering Snape's love for Harry's mother.
As the story progresses, they might start to work together more closely. Snape could be teaching Harry some advanced magic that no one else knows, and through this process, they build a bond. Harry begins to understand Snape's past better and realizes that they have more in common than he thought, like their love for Lily Potter in different ways.
In fanfiction, their relationship can develop in many ways. Sometimes it starts with Harry being suspicious of Snape as in the original books, but then Snape shows his selfless side. For example, he might save Harry from a dark spell and that starts to change Harry's view.
The development could also be due to the way the author writes Snape's backstory in the fanfic. If the author delves deeper into Snape's past, his difficult childhood, and his love for Harry's mother, Harry might start to understand Snape better. This understanding leads to admiration as Harry realizes that Snape is not just the strict and seemingly cruel professor he thought he was.
Their relationship could develop from pure hatred to grudging respect. Harry may come to understand Snape's difficult position in the wizarding world and Snape might see Harry as more than just James Potter's son. For example, Snape could start to appreciate Harry's courage and determination during their time together in the summer.
Their relationship development is complex. Snape, being Harry's guardian, has to deal with his own past issues regarding Harry's parents. Initially, Harry is very suspicious of Snape's motives. However, as time goes on, Snape starts to share some of his knowledge with Harry, especially about potions and the darker aspects of magic that he thinks Harry needs to know for self - defense. This sharing of knowledge gradually breaks down the barriers between them. Also, Snape might start to involve Harry in some of his personal projects related to protecting Hogwarts, which makes Harry understand Snape's dedication to the school and to him in a new light.
Their relationship develops in a rather interesting way. Snape, being a strict mentor, forces Harry and Draco to look past their differences. Harry begins to understand Snape's past and the reasons for his actions, which in turn makes him more open to Draco. Draco, who has always been in Snape's good graces to some extent, has to adjust to sharing Snape's attention with Harry. This causes some initial jealousy but later leads to a sort of rivalry - turned - friendship as they both grow under Snape's tutelage.
At first, it's likely to be very tense. Snape has always had a grudge against Harry because of his father. But as they live together, they start to see each other's true selves. Harry might see Snape's vulnerability and intelligence, while Snape might see Harry's courage and determination that are different from James's arrogance.
Often, it starts with intense dislike. Snape is constantly critical of Harry in class, deducting points for the slightest mistakes. Harry, in turn, sees Snape as a bully. As the story progresses, there might be small moments of grudging respect, like when Harry realizes Snape's intelligence in potions, but the overall hatred remains for a long time.