I know that the Sorting Hat wanted to for other reasons, but if he made the right decision then why did he ever want to? The Sorting Hat made it very clear that he chose the right house, then why did he ever consider putting Harry in Slytherin?
The Sorting Hat was picking up on the Dark Lord’s soul in Harry.
It’s hinted that the reason that the Sorting Hat was considering putting Harry in Slytherin was because of the piece of Lord Voldemort left inside of him.
“You can speak Parseltongue, Harry,’ said Dumbledore calmly, ‘because Lord Voldemort – who is the last remaining descendant of Salazar Slytherin – can speak Parseltongue. Unless I’m much mistaken, he transferred some of his own powers to you the night he gave you that scar. Not something he intended to do, I’m sure …’
‘Voldemort put a bit of himself in me?’ Harry said, thunderstruck.
‘It certainly seems so.’
‘So I should be in Slytherin,’ Harry said, looking desperately into Dumbledore’s face. ‘The Sorting Hat could see Slytherin’s power in me, and it –”
- Harry Potter and the Chamber of Secrets, Chapter 18 (Dobby’s Reward)
This is confirmed in an interview with J.K. Rowling, when she says the Sorting Hat was strongly tempted to put Harry in Slytherin because of the piece of the soul.
Also, I always imagine that the Sorting Hat detected the presence of that piece of soul (JN: Yeah!) when Harry first tried it on, because it’s strongly tempted to put him in Slytherin. So that’s how I see it.
- Pottercast interview (Dec 23, 2007)
The Sorting Hat had decided not to put Harry in Slytherin at least somewhat in part due to Harry’s own desire not to be in Slytherin - but it seems fairly clear that the reason the Sorting Hat was considering putting him there to begin with was because he was “seeing” the Dark Lord’s soul as a part of Harry and that part seemed to be suited for Slytherin.
Destiny for greatness
Because you know what Salazar Slytherin looked for in his chosen students? The seeds of greatness (Pottermore)
Harry was destined for greatness. Both in-universe (by the time of Sorting, he was told so by Ollivander upon picking the voldemort-phoenix wand). And fourth-wall, as we know he ended up ending Riddle in the end and generally was a great hero.
- Harry has "a certain disregard for the rules" (As per Dumbledore in CoS). A very Slytherin "the end justifies the means" mentality.
Not only was Potter Destined for Greatness and wasn't a rule follower, he also had the psychological disposition of an abused child wanting to achieve something to make his abuse worth it. Harry had the ambition, cunning and resourcefulness to cut and run when he needed to to avoid Dudley or his bully friends. He is a born leader and he had an innate highly developed senses of self-preservation (When his magic would protect him).
Probably the Sorting Hat listened to his request because he isn't seeking fame, he isn't very clever, he is not self-assured nor is he confident of his own competence. Nor is Harry one to fall deeply into unrequited love like the Bloody Baron, Snape and Bellatrix. There are two more examples if you assume Merope would have been Slytherin if allowed to go to school and if you acknowledge Draco having a crush on Hermione with inappropriate expression of said feeling