Well, perhaps in this fanfiction, Harry might be seen as a special case that confounds the Sorting Hat. Maybe the hat simply can't detect his true nature due to some magical interference or a unique quality within Harry that it has never encountered before.
One possibility in the 'harry can't be sorted fanfiction' is that the Sorting Hat tries multiple times to sort Harry but fails each time. This could cause a stir among the students and faculty. Harry might feel left out or confused as all his peers are sorted into their respective houses. There could be speculations that he is some sort of prophesied figure whose path is not meant to be defined by the traditional house system. Maybe there are dark forces at work that are preventing his sorting to disrupt the normal order at Hogwarts.
In the 'harry can't be sorted fanfiction', it could be that Harry's experiences prior to the sorting ceremony have so muddled his identity that the Sorting Hat is unable to place him. For example, if he has been exposed to a wide variety of magic from different houses already, the hat might be at a loss. It could also lead to a situation where the Hogwarts staff has to figure out an alternative way to house Harry, which could involve him being a sort of 'free agent' among the students, or perhaps they create a new, special category just for him.
Well, he might face some initial doubts from the members of Phoenix House. They could be wary of his fame. But as time goes on, he would prove himself by showing his loyalty and unique skills, like his great flying abilities and quick thinking in the face of challenges.
Well, he might face a lot of challenges. In Slytherin, he'd be surrounded by students with different values compared to Gryffindor. He could have a tough time making true friends at first. But it might also give him a chance to change the perception of Slytherin from within. He could use his Gryffindor courage to influence the more cunning and ambitious Slytherins towards a more positive path.
The fact that Harry is sorted into Ravenclaw could also cause a rift with some of his Gryffindor friends at first. However, as time goes on, they could come to see the benefits of his new House. Harry might introduce some Ravenclaw values like open - mindedness to Gryffindor. And his Ravenclaw housemates could also learn about loyalty and bravery from Harry. This could lead to a more united Hogwarts against Voldemort, with all the Houses working together in new ways.
If Harry gets sorted into Ravenclaw in fanfic, he would likely face a whole new set of challenges. He'd have to adapt to the Ravenclaw house values which are different from Gryffindor's. His relationship with Hermione could be interesting as they'd both be in different houses yet share a love for knowledge. He might be more isolated from Ron at first, but this could lead to new character growth as he makes friends within Ravenclaw.
Well, T'Challa could teach the Hogwarts students about Wakandan self - defense techniques. This would be a new and exciting addition to their curriculum. Maybe he'd even start a new club for it.
Obviously, Harry would be a main character. Since it's about him not being sorted. Dumbledore would probably also play an important role. He might be the one trying to figure out what to do with Harry in this strange situation.
In fanfiction, if Snape was sorted into Gryffindor, he might have had a very different relationship with the Marauders. Instead of being their rival from Slytherin, he could have been a part of their group. He may have been more open about his emotions and not as bitter as he was in the original story. His relationship with Lily might also have developed in a more positive way without the house rivalry constantly straining their friendship.
Well, perhaps in this fanfic, the fifth house could be a house for those with mixed magical abilities. Harry might be sorted into it because he has both Gryffindor - like courage and Slytherin - like cunning. He could then meet new friends who also don't quite fit into the traditional four houses. They would go on adventures together, facing challenges that require the unique combination of traits that the fifth house represents.
Well, it could be that Harry's glasses are actually in the possession of a dark wizard who wants to disrupt Harry's life. Without his glasses, Harry would struggle to see clearly and defend himself. However, with the help of his friends, he might be able to track down the dark wizard and retrieve his glasses. This could lead to an epic battle or a series of clever magical maneuvers to outwit the enemy.
There are quite a few such fanfictions. One popular one is 'The Secret of Ravenclaw' where this plot twist occurs.