Most people interpret Shelock's "tantrums" as immature and think that his "bad" behavior is a sign of his supposed lack of empathy. John knows it's easier to believe that Sherlock is a "high functioning sociopath" than to examine one's privilege and change one's expectations of proper behavior.
That's the thing that makes John a better candidate for his flatmate than most - John's a doctor. And just as Sherlock is good at deducing, John is good at diagnosing.
For one, there's no such thing as a high functioning sociopath and even if there was, he's seen Sherlock's empathy. It was a short moment, just after John insinuates that he knows what he'd say as he was dying because of the war. It's obvious by the look on Sherlock's face that he's utterly horrified, but Sherlock's complete and utter focus on the Work renders all outside information useless. The second Sherlock realizes he's done wrong, it nearly paralyses him, so the quick change in subject doesn't bother John in the long run; if he'd focused on the embarrassment, it'd take up all his resources. Besides, it's further confirmation of his suspicions.
For another, John can see other signs too. His "stimming" is atypical, but fits with someone who has been taught "socially acceptable" alternative behaviors. His controlled movements belay a sense of practice, as well as a fear of losing control. Then there's his obsessive thought patterns and the way he loses the sensation of hunger or pain when he's concentrating on Work.
He also reacts to overstimulation in stereotypical ways - shutdown or meltdown. John sees the near catatonic behavior early on; Sherlock's so focused on sorting out the details that he won't move for hours on end and then he needs John to send a text for him. It's as if he can't move for fear of losing his entire train of thought and his verbal ability seems reduced during that time too. A meltdown shows up during the drug bust - there are so many people talking and these people are trying to shame him in front of his new potential flatmate and it'd be overwhelming to the typical person, but for Sherlock? He probably hears every scuffle of feet, the light bulb that make a soft buzzing noise, smells everyone's cologne and perfume, feels every little tremor on the floor and this is on top of the embarrassment and people talking and understandably, Sherlock strikes out.
It's not that John would tell Sherlock right out that he sees what everyone else ignores; he didn't particularly care for it when Sherlock did it to him on their first meeting. Instead, he sneaks in conversations about how it's not appropriate to smile at crime scenes and he doesn't "correct" Sherlock's typical stimming when it appears and he insists on checking Sherlock for wounds after a big fight and does all the little things that need to be done to keep Sherlock healthy.
To John, as frustrating as Sherlock can be at times, the people around Sherlock seem more heartless than him. As far as he can tell, no one has really tried to understand Sherlock's behavior. Sherlock does care about people, but it's expressed in such an atypical way that people miss it. But because they think Sherlock doesn't have a heart, they treat him in the most cruel and hurtful ways and somehow come away thinking they're not being terrible people.
It's a disheartening thing to realize, but as John falls farther into their friendship, the more he feels a need to protect Sherlock from these things. Because even more disheartening? Sherlock has probably been treated this way his whole life. He's likely dealt with bullying not just for being smart, but also for not understanding the social conventions that "everyone" knows.
When Moriarty comes after Sherlock, he tries to make everyone believe that Sherlock has been behind all these crimes and all John can seem to worry about is how other people will see Sherlock from now on, that they'll be even more inclined towards cruelty. He realizes just how far he'd go to protect Sherlock isn't normal, not as "just" his flatmate or "just" his friend. He looks at Sherlock and realizes he's in love and it's shocking and it's scary.
And as he watches Sherlock jump, as he sees him fall and fall and fall, John can't help but think about their last conversation, the one in the lab, and he wonders how he could be just as terrible and heartless as the rest of them.
A/N:
1) As someone who has worked with people with developmental disabilities (including autism), I saw signs of Sherlock being on the spectrum from the first episode (though I missed the stimming at first). These feelings were recently confirmed when I read meta on the subject written by someone with autism and I'm pretty sure everyone who loves Sherlock (the show, the character) should read these essays. Check out the username "street-howitzer" on tumblr - it's "The Slumber of Feelings" link on the right hand side.
2) To the anon before I turned anon reviews off (I don't like not being able to respond, good or bad), I'd like to say that I'm not excusing Sherlock of hurting other people's feelings, but rather, I don't think he's cruel and heartless for "no reason." I read him as autistic and so do a lot of people, hence the "defenses," which I view as explanations that do not excuse him of wrongdoing, but offer insight into why he some times acts in a way that other people view as rude, hurtful, etc. Anon and those who share the same opinion should really check out the meta I referred to above (especially parts 3a and 3b) and check their fucking privilege before just spouting off bullshit. Please consider the fact that most of Sherlock's behavior is generally provoked (Donovan and Anderson, in PINK, they're terrible and rude to him and try to make John think less of him, and he responds in kind, not the other way around) or accidental (the scene in PINK that I refer to in the third paragraph). Finally, just as there's no such thing as a "high functioning sociopath," there's no such thing as a "borderline sociopath" and actually, a lot of people with autism self-diagnose themselves as high-functioning/borderline/etc sociopaths before getting a correct diagnosis.
While I've generally gotten a warm and positive reception for this fic, I was angered by this comment (because it reeks of the exact same privilege and cruelty that I was writing about in this fic) and I did feel like I needed to clarify that I'm not saying that Sherlock's lack of social understanding means that he's suddenly absolved of any hurtful words and/or behaviors.