In fanfiction, the author might want to explore Snape's past more deeply. Maybe there are events in his life that could have made him truly side with Voldemort. For example, if he had been more influenced by the dark arts from a younger age or had different relationships with other dark wizards that pushed him towards Voldemort. Also, it could be a way to show how different choices could have changed the whole 'Harry Potter' story.
In some fanfictions, Snape may be depicted as truly on Voldemort's side. Fanfiction allows for creative reinterpretations of the original story. However, this goes against his complex and ultimately heroic role in the official 'Harry Potter' series. In the canon, Snape was a double agent, secretly working against Voldemort to protect Harry and help bring down the Dark Lord.
One possible reason could be that Snape fails to deliver crucial information. Voldemort is a very demanding and unforgiving master. If Snape doesn't give him accurate details about the Order of the Phoenix's plans, for example, Voldemort would surely be enraged and punish him.
One reason could be for comical effect. It's quite funny to think of the powerful and feared Voldemort as a pet. Another reason might be to explore a different power dynamic. If Voldemort is a pet, Harry has a certain level of control over him, which is a complete reversal of their normal relationship in the original story.
One reason could be a prophecy misinterpretation. Voldemort might initially think that Harry is key to his success in a different way than he originally thought, and so he saves him to figure out this new angle. For example, if there was a prophecy about a 'chosen one' and Voldemort realizes he needs Harry alive to fulfill some part of it that benefits him.
Some fanfiction writers might create this concept just for the sake of being different. They want to explore a completely new and shocking relationship that goes against the norm of the original story.
One great fanfiction on this topic is 'The Dark Trials of Snape'. It really delves into Snape's inner turmoil as he endures Voldemort's torture. The author does an excellent job of portraying Snape's complex emotions and his unwavering loyalty to Dumbledore even in the face of such horror.
Snape might endure the punishment in stoic silence. He is a complex character and often used to hiding his true emotions. So, he could just grit his teeth and bear it, all the while plotting his revenge or a way to get out of the situation.
The possible reasons are numerous. For starters, fans might be interested in exploring the idea of how two very different characters like Snape and Hermione could be related. It could also be a way to give Hermione a more mysterious origin. Since Snape has such a complex and often misunderstood character in the original series, tying him to Hermione in this way can create interesting storylines. Additionally, it might be a form of wish - fulfillment for some fans who want to see a different kind of family structure in the Harry Potter universe.
One possible reason is Snape's prejudice. He might have some sort of bias against Gryffindors in general, and Hermione, being a very Gryffindor - like student, gets the brunt of it. He may expect her to make mistakes typical of Gryffindors like being overly bold without thinking. Another factor could be that Hermione is so intelligent and inquisitive that Snape feels threatened. He likes to be in control of the knowledge in his classroom, and Hermione's constant questions and thirst for knowledge might make him act tough towards her.
A creative reason could be a magical prank gone too far. The Marauders or some other mischievous students play a prank on Snape using a new, untested spell. The spell backfires and Snape ends up in a state where he needs to be diapered. This would lead to a story of revenge, forgiveness, or just chaos at Hogwarts.