Often, Harry's response is a mix of hurt and determination. The hurt from Snape's actions can cut deep, but it also fuels his determination to prove Snape wrong. He may strive to become better at magic, especially in areas where Snape has criticized him. He might also start to question Snape's loyalty to Dumbledore, suspecting that there's more to Snape's actions than meets the eye. This could lead him on a journey to uncover the truth about Snape in the fanfiction world.
In some fanfictions, Harry might cope by finding solace in his friends at Hogwarts. He could talk to Hermione and Ron about what Vernon does, and their support gives him strength. For example, they might encourage him to focus on his magic studies as an escape from the Dursley's household.
One common reason could be his pride. Snape has a lot of pride, and in some fanfictions, this pride might prevent him from admitting his true feelings to Lily. Instead, he lashes out and ends up hurting her. Another reason could be the pressure from the different sides he's associated with. He's in a difficult position between the Death Eaters and the Order of the Phoenix, and this stress can make him act out towards Lily.
In some fanfics, Snape might hurt Harry out of his long - held grudges. Snape was in love with Harry's mother, Lily, and Harry being a reminder of James, who bullied Snape in school, could trigger his negative emotions. Also, Snape's loyalty to Voldemort in the earlier days in some fan - created scenarios might lead him to target Harry, who was seen as a threat to Voldemort's plans.
However, as the story progresses, Harry may start to understand the reasons behind Snape's actions. He could become more resigned and accept the punishment as a part of his growth. He might use the experience to become more cautious in his actions and more respectful of the rules.
In some fanfictions, Snape might punish Harry by giving him extra detention tasks like scrubbing the cauldrons in the Potions classroom until they shine. This is a common form of punishment as it's within Snape's domain as the Potions master.
One common reason is Snape's lingering hatred for James Potter. Since Harry looks so much like his father, Snape might take out his old grudges on Harry. He sees James in Harry and can't help but be reminded of the past bullying and his unrequited love for Lily. So, he acts hurtfully towards Harry as a way to get back at James, even if it's not really fair to Harry.
Maybe Snape suspects Harry of being involved in some sort of dangerous activity related to the Dark Arts. Pressing him to the wall could be a way to force Harry to come clean about his actions or any knowledge he might have. It could also be that Snape is acting out of his own insecurities and pent - up emotions towards Harry, which he has been suppressing for a long time.
In some fanfics, at first it gets worse. Harry might start to fear or hate Snape even more after being hurt. But as the story progresses, there could be a turning point. Maybe Harry discovers Snape's real motives behind the hurt, like if Snape was trying to protect him from a greater danger in a very roundabout way. This could lead to a begrudging respect or even an odd sort of friendship in the end.
One possible reason could be that Snape is trying to intimidate Harry. He has always had a rather tense relationship with Harry in the original story, and this could be an extreme form of showing his authority. Maybe he suspects Harry of something, like being involved in some mischief or having knowledge about a certain Dark Arts item or activity.
In some fanfictions, Snape might awkwardly try to comfort Harry. Given his own complex personality, it wouldn't be an easy or natural gesture for him. He might pat Harry's shoulder stiffly or offer some gruff words of reassurance like 'Pull yourself together, Potter.'