Dumbledore tells Severus that he thinks they sort too early, but for all his knowledge and wisdom, the old man never understood.
The sorting hat is sentient, Gryffindor's greatest achievement right after his role as founder of Hogwarts. A simple hat, old and wrinkled after years of intense use ended up as the greatest magical artifact, trumping even the Philosopher's stone. It had always been Godric's favorite piece of cloth.
The inside of the hat, which nobody has ever taken the time to look at (, not that Gryffindor's enchanted object would have let them), is inscribed with the most powerful tamed magic wizards and witches possessed a millennium ago. Runes cover every available inch of cloth. Like Hogwarts itself, the Sorting hat has absorbed the oppressive magic that forms in the air in the presence of great numbers of magical beings. The abilities it has are hidden from everybody, even the headmasters. The four Founders themselves were unaware of what they'd created beyond a fairly complicated personality sorting spell.
These years, it sees the infinite possibilities that the separation of the children into four separate factions supply. The placement of a single girl or boy can change the future drastically. Not only the child's own, but also that of friends and enemies he or she makes and doesn't make.
The hat has two responsibilities, of which number one will always precede number two. One, to keep Hogwarts accessible to every child who wants to be there, no exceptions. Hogwarts must remain open, even during times of war. Two, the happiness of each individual child. It fails far too often at the second.
Hermione Granger, who is forgotten in Ravenclaw, smart but too bookish, standing out because of her intelligence, but also shunted for it by the jealous eagles. She dies far too soon to mean anything, her unlimited potential fading with her life. As a lion however, she stands beside Harry Potter as the smartest witch of her age, surrounded and protected by friends and family she never would've made otherwise. Learned from her best friend that books aren't everything, and that sometimes the rules have to be broken to keep the world from going up in flames.
Neville Longbottom, the badger that locked himself away in his greenhouses, never getting the chance to prove to others – though more importantly himself - that he is not a squib. The boy who never loses his clumsiness or finds his confidence, who remains ashamed of what his parents were forced to be, and never learns that he had been one choice away from taking over Harry Potter's role as the boy who lived, though maybe he is thankful about the latter. Neville in red, who stood up against his friends to keep them safe, who earned the 10 points that handed Gryffindor the House Cup in his first year, who lead a rebellion and killed the snake that kept Voldemort's soul attached to earth.
Severus Snape, who never had a place in Gryffindor as he was cunning and ambitious, hungry for not power, but recognition. Snape, the definition of a Slytherin, courageous only in his selfish selflessness. The man who gave his life for a boy he hated for the woman he loved. The master spy who was the embodiment of Salazar himself, and belonged with the snakes without question. The boy the sorting hat placed with those like him, uncovering his full potential, but leaving a tortured soul in the end because he had a role to play in his rightful house. Though he would have been happy with the lions. No, not the lions, Lily, just Lily would've been enough. The suffering of one to prevent the death of thousands. Dumbledore's Greater Good. The hat still wishes he had placed the boy with his only friend, consequences be damned.
Sirius Black, who became the greatest Death Eater and stood at Voldemort's right hand, never getting a chance to pull away from his family. Insanity in his eyes, surpassing even his cousin Bellatrix as he rashly slashes through the ranks of the Order and his kin alike. A deadliness he never had the opportunity to tame, guilt he never felt, because Blacks don't have friends to be their conscious. His traitorous brother dead at his own hand, himself the favorite of his mother, though he couldn't care any more in that universe than his Gryffindor version. Sirius deserves the group of friends he gains the least, but he gets them, because Hogwarts would be in rubble otherwise. The elder Black brother learns quickly enough under the guidance of his black-haired friend, regressing only when he finds the bodies of James and Lily, nothing holding him back. Black behind bars is the safest for everyone. Regretfully, even Remus Lupin agrees. At least the not-very-white sheep of the Black Family dies for something worthy.
Tom Riddle himself, who would have not been noticed in Hufflepuf or Ravenclaw or Gryffindor, though he easily fit with the first two houses, hard-working and extremely smart. Even Dumbledore would've forgotten him until it was too late, until his followers were many and the Ministry unknowingly burning at his feet while he took the throne and destroyed the world. The snake-version is watched closely by his Transfiguration teacher, suppressed by his pure-blooded companions until he proves himself descendent of their founder himself. The set-back takes enough time that Harry Potter can be born to take him down. The hat knows of the Prophecy long before Trelawny recites it. It is almost sentient enough to wonder if he projected it to the seer in the first place.
Peter Pettigrew, who had neither bravery, cleverness, loyalty nor cunning. Nevertheless the rat ended up in Gryffindor, because he would shape the others for the battle yet to come, at least useful in the end. This way, he can help Lupin during the transformations, who has his own part to play, and shapes the futures of both Black and Snape directly. The young werewolf will have more impact on the world than he will ever realize.
Percy Weasley, the ambitious redhead that never had a chance to belong in his family after his placement in Slyherin. Who reaches greatness and could have restored the good standing of the Weasley name, had he not taken the Dark Mark in his search for power. The young man who hesitantly tells his friend Marcus of the Burrow, which is torn apart that same Christmas Eve, the family he hasn't spoken to in years inside when the already shabby structure collapses at the first explosion. He has a spot in Slytherin, but gets sent to the house with his brothers and later his sister, so he would take his place with the family he denies being related to for years to come, until he learns that he doesn't want to be a Weatherby. He finds his courage and his own role eventually, just in time, but in time nonetheless.
Regulus Black, who belonged with the lions more than his brother ever would. His bravery in the face of death had been inside him all along, even at eleven. The boy who will change the world every way he goes, who is not the smartest, but definitely the cleverest. The boy with the political cloud of a Black, but who inexplicably didn't inherit the genetic madness that runs in his inbred family. The young man dies forgotten, his secrets taken to his grave. Even with Voldemort's poisonous liquid running through his veins, he laughs as the inferi drag him down to the bottom of the lake, Kreacher long gone with the Locket Horcrux. In that moment, he is insanely sane, his mind clear and the hat might not understand it yet, if it ever does, but Regulus Black dies happier than he otherwise would.
Harry Potter, the boy-who-lived, arrives on the stool with a mantra in his mind. He begs for an alternative to Slytherin. The green-eyed boy understands far less of the Soring Hat at age eleven than Dumbledore, but he learns. The hat only knows this because little Albus, his father's and grandfather's twin in appearance, shows him the memory of an insignificant conversation. Like his dad, Albus pleads with closed eyes for any other house than Slytherin.
Back when Harry was sorted, the hat had asked him to at least consider the snakes, because despite every role thrust upon the child, he had to save Draco Malfoy to accomplish his goals as well, and the separation between the two rival houses was too big to consider friendship. The hat learns that Harry Potter doesn't need Malfoy's friendship to save his life and hands him happiness and peace in the future to come. The boy-who-lived could've been great, but he chose to be loved.
Today, when Albus Potter asks the same, there is no need for discussion. The son is undeniably a better man than his father, having been taught by the best. House prejudices will not prevent the young Potter from doing what has to be done, from crossing boundaries and uniting the school for another war to come.
A/N I'm pretty sure I got all the dubious sortings, if you can think of another, let me know!