One common reason could be his love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him out of his undying love for her. It's like he's trying to preserve a part of Lily that still exists in the world through Harry.
In some fanfictions, Snape could have a change of heart about Harry over time. Maybe as he gets to know Harry better, he realizes that Harry is not just James Potter's son but an individual worthy of protection. Harry's courage and goodness might shine through and make Snape want to safeguard him.
Snape might also see Harry as a key to defeating Voldemort in the fanfiction. Knowing Harry's importance in the fight against the Dark Lord, he protects him to ensure that the wizarding world has a chance at peace and freedom from Voldemort's tyranny.
One reason could be that Snape has his own complex sense of loyalty. He may feel that Dumbledore's plans for Harry are too dangerous or not in Harry's best interest in some ways. He has a long - standing relationship with Harry's mother, Lily, and perhaps through that connection, he wants to safeguard Harry from any harm that might come from Dumbledore's actions or decisions.
Well, he might use his magic skills. Maybe he creates some protective spells around Harry to keep the werewolf at bay. For example, a strong shielding charm that can withstand the werewolf's attacks.
In some fanfictions, there could be other dark wizards or witches who are allied with Voldemort or have their own reasons for wanting to harm Harry. Snape would have to protect Harry from these various threats as well. For example, some Death Eaters might try to take matters into their own hands and go after Harry without Voldemort's direct orders.
In the fanfiction, Snape could protect Harry from Dumbledore by using his skills in potions. For example, he might create a potion that hides Harry's magical signature from Dumbledore's detection. Or he could use his knowledge of the Dark Arts to counter any spells or charms that Dumbledore might use to keep tabs on Harry. Snape is very intelligent and resourceful, so he could find various ways to physically and magically shield Harry from Dumbledore.
Another reason might be that Harry is suspected of sneaking around in areas where he's not supposed to be. Snape, as a vigilant teacher, may punish Harry to maintain discipline in the school. He may think Harry is up to something related to the ongoing dangerous situations in the wizarding world and wants to keep him in line.
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.
One possible reason could be Snape's long - standing grudge against James Potter, Harry's father. Since Snape had a difficult past with James, he might project that onto Harry. Another reason could be that Snape is trying to protect Harry in a very strange way. He may think that by rejecting Harry, he is keeping him at a distance from the dangerous wizarding world politics and plots that Snape is often involved in.
In some fanfics, Snape might punish Harry because of his perceived insolence in class. Harry has a rebellious streak, and Snape, being strict, wouldn't tolerate any behavior that he deems disrespectful to his authority as a teacher.
Well, perhaps there was an emergency at Hogwarts. Maybe some dark forces were approaching, and Snape, being a powerful wizard and a Hogwarts professor, felt it was his responsibility to pick Harry up. Harry was always a target for the dark side. Also, it could be that Snape had some new information about Harry's family or his destiny that made him decide to take Harry under his wing, so to speak, by picking him up.
One possible reason could be his lingering resentment towards James Potter, Harry's father. Snape and James had a long - standing feud during their school days. Since Harry looks a lot like James, Snape might be transferring his old grudges onto Harry.