One reason could be for the sake of character exploration. Writers want to see how Harry would develop if he embraced different, often 'feminine' qualities. It adds a new dimension to his character.
It might be a way to subvert the traditional gender roles in the Harry Potter universe. By having Snape feminize Harry, it challenges the typical masculine image of Harry as the hero and shows that he can have a more complex personality. In some fanfics, this can also be used to explore relationships in a different light, for example, how Snape and Harry's dynamic changes when Harry exhibits these new traits.
Some writers may be interested in exploring the idea of masculinity and femininity in a magical context. The wizarding world has its own set of norms, and by feminizing Harry through Snape's influence, they can play with how these concepts interact with magic. For example, a feminized Harry might use magic in a more intuitive or gentle way, which is different from the more forceful approach often associated with his male character in the original series.
In certain fanfic scenarios, Snape may feminize Harry by influencing his appearance. Maybe he gives advice on clothing or grooming in a way that makes Harry seem more feminine. For instance, suggesting a more delicate style of robes or a different hairstyle that is associated with femininity in the wizarding world.
Some authors write these fanfictions to show different sides of the characters. For example, Snape's action of hitting Harry could be a result of his own inner turmoil, perhaps related to his loyalty to Dumbledore and his hatred for James Potter. By writing about this, they can show Snape in a new light. Also, it can show Harry's growth in dealing with such a difficult situation. He can either become bitter or try to understand Snape's motives, which are interesting character development arcs.
Some 'Harry Hurts Ginny' fanfics exist because it adds a new layer of drama to their relationship. Their relationship in the original series was mostly positive, but exploring the negative aspects like Harry hurting Ginny can make for an interesting and complex story.
Some 'Hermione breaks Harry' fanfics exist because it offers a new and different take on their relationship. The traditional view of their friendship is so strong that exploring a break in it creates a lot of drama and emotional tension, which is interesting for readers.
Some fanfictions like 'Harry Potter hides as a girl' exist because it's an interesting 'what - if' scenario. It allows authors to explore different aspects of the Harry Potter universe in a new light. They can play with the character dynamics and how the story would change if Harry had this different identity.
Some fans might feel that Dumbledore was too manipulative in the original series. They create these fanfictions to explore an alternative view where his actions are not excused.
The relationship between Harry and Snape is full of tension and mystery in the original books. Fanfics give writers and readers the chance to rewrite or expand on that relationship. For example, some fanfics might show Snape as a more positive influence on Harry's life, which is different from what we mostly see in the books.
These fanfics are appealing as they often delve deeper into Snape's character. We know he had a difficult past, and seeing him in a paternal role gives him a chance at redemption and growth. Also, the relationship between Harry and Snape was always full of tension in the original books. Changing it to a father - son like bond in fanfics creates a sense of warmth and hope that many readers find attractive.
Many 'Snape Saves Harry' fanfictions exist because the relationship between Snape and Harry is so complex and full of potential in the original 'Harry Potter' series. Snape is a very ambiguous character, and his saving of Harry in the main story is a major plot point that fans love to explore further. They want to see different scenarios and motives for his actions.
Some exist because some fans really ship Harry and Hermione (HHR) and feel that the Weasleys, especially Ron, are in the way of their ideal pairing. So they create fanfics to bash the Weasleys to make their preferred relationship seem more likely.