I believe Snape is autistic
(FYI: I’m autistic myself and I have autistic children.)
He’s lonely. He doesn’t really have friends. We know of Lily, we also hear about Lucius Malfoy, but we don’t really see their friendship which in my opinion is much less close than fans believe. As a student he’s so alone that no one but Lily tries to stop the bullying.
He doesn’t participate in any social meetings. He’s quite miserable during the Christmas in Harry’s third year. He patrols the corridors and the grounds instead of attending the Yule Ball. He doesn’t stay for dinner after the Order meetings. He only attends the DE meetings because he has to.
His peers at school think he’s weird. Lily’s friends from Gryffindor don’t understand why she’s friends with him. When Harry asks why the Marauders bullied him, Sirius says he was different, weird, he was an "oddball". Autistic children and teenagers are often bullied because they are perceived as not normal, awkward, weird.
He doesn’t make a normal eye contact, he stares a bit too much. It can be partly explained by Legillimency, but he stared too much even as a teenager.
There’s a diffeence between how he speaks as a teenager and as an adult. It doesn’t sound entirely natural, he definitely had to put effort into that. It’s partly because he doesn’t want to sound like a poor man with a northern (?) accent, but autistic struggle with fluent communication may also be a reason.
He’s quite rude. He might be just *evil*, but he may just not fully understand how cruel he actually sounds. From his point of view he’s just honest and doesn’t beat around the bush. OK, maybe he’s a little mean, but not cruel… right?
He uses sarcasm (a lot of autistics actually do), but he doesn’t really appreciate Harry’s and other people’s sass, he treats their words too seriously.
He usually speaks coldly / calmly / without much emotion.
He’s usually dispassionate, he has limited facial expressions. Many autistic people also have a "resting b!tch face" unless they try to look more "normal". Perhaps he isn’t always as hateful as Harry thinks, perhaps it’s just his face.
He seems a little oblivious to other people’s emotional state and seems to analyse their behavior more intellectually.
He has special interests: Dark Arts / DADA and Potions.
His Potions ingredients must be very orderly, he knows immediately that something is missing and what it is.
He "loves" rules. Students are breaking the rules? He takes points or gives detention. The Marauders are bullying him? He wants them expelled. (While Harry deals with the bullies on his own.) He’s caught Sirius whom he believes to be responsible for Lily’s death? He’s going to hand him over to the Ministry and the Dementors. (While Sirius and Remus want to murder Peter themselves.)
Since Snape likes rules and order, Harry who is a bit wild and unpredictable annoys him.
He doesn’t wash his hair as often as he should. It could be partly because of his poor background (he was neglected, he wasn’t taught to take a proper care of his hair, he didn’t even have a real bathroom as a child), partly because he has no one to look nice for, partly because of the Potions fumes. Autism might make him care less about his appearance. (He does care about hygiene though. Apparently he shaves regularly and Harry would certainly notice if Snape was dirty or smelly. His sallow skin and teeth have nothing to do with hygiene, it’s a result of his poverty and malnutrition.)
During the Occlumency lessons he’s touching his lips with his finger while he’s thinking.
He has some sensory issues. He wears the same, a little baggy robes (they flutter as he walks). He’s sensitive to light: his Potions classroom is dim (it’s in the dungeons, but he could brighten it up with magic); he makes his DADA classroom dim, even though it’s no longer in the dungeons; when Harry comes to his first Occlumency lesson, Snape waits for him in a dark room. (You know, people don’t do things like that because they’re evil, it doesn’t make sense).
John Nettleship whom Snape was partly based on was probably autistic.