One of the banes of the modern Watson's existence, in Sherlock, is that the public at large are constantly mistaking him for Sherlock's date. It happens from the very start; when they go to look at the apartment, Mrs. Hudson mentions that there's a second bedroom upstairs "if you'll be needing it", and when they use a restaurant as cover for a stakeout, the owner offers to get the table a candle on the grounds that it's more romantic. The sheer repetition is what pushes it into funny territory -- and then out of funny territory again in places, like when John's erstwhile girlfriend starts believing it -- and the fact that two of the first people to make the mistake are people who have evidently known Sherlock much longer than he has make John squirm a bit and make a most awkward, but very diplomatic, attempt to ask Sherlock if he is being flirted with and failed to notice.

The attempt to clarify makes Sherlock wonder if John has been flirting and he failed to notice, which brings on his even more awkward but strangely diplomatic effort to turn John down nicely. This is rather interesting, both because it's very rare for Sherlock to make any effort to interact with anyone using standard scripted social behavior, and because to date John is literally the only person to whom he has ever acknowledged that it's possible that this is the impression he's making, and who has gotten a surprisingly clear explanation of what impression he's actually trying to make.

John corrects people constantly, or tries to. Sherlock doesn't even acknowledge that people are making the assumption. It's not even clear whether he realizes that when he tells people John is his friend, said people infer that John is his "friend"; many people assume quietly, which John spots because he's used to interacting socially like that, but even when they say things that are obviously predicated on the idea that Sherlock and John are romantically involved, Sherlock just edits out the statement before it gets past his ears and responds to other parts of the conversation.

Why the people who know Sherlock sort of casually make the mistake is easy to explain: Sherlock does a lot of unSherlock things when interacting with John, like sincerely paying attention to the various talky noises coming out of John's mouth, and sometimes even modifying his behavior based on them. When normal people suddenly begin to be deeply invested in things someone else says, particularly when they never gave two-tenths of a shit about the subject before, it means that they are desperately trying to get that person's attention and subsequent approval. The reason for this can vary with gender, age, relative social status, and other things, but nine times out of ten they desperately want this person's attention because they are hoping to engage in a lot of pants-optional adult activities with said person sometime in the near future.

Why strangers do this is down to more or less the same thing Molly was talking about when she told Sherlock he looked sad whenever he thought John couldn't see him. Unless he's specifically policing his reaction, Sherlock looks to John for a lot of social and emotional cues. He's learned that John will answer the questions that make people like Sally Donovan think he's a sociopath. (What Donovan takes for a total lack of empathy is mostly ignorance; Sherlock has spent a lot of time rejecting as illogical, or flat not paying attention to, a lot of unspoken social rules. Oftne he just doesn't know what reaction others would consider appropriate -- the only way he can figure them out at this point is to ask, and when people like Donovan freak out at him, they don't answer the goddamn question.) He's also learned that for whatever reason, John is much better at reading what his mood is than anyone else, and if he looks to John for something, John's reaction will reflect back whether what Sherlock is doing is something that's likely to get him into trouble. Consistently turning to a particular person for emotional feedback is a sign of attachment, and one Sherlock doesn't show with other people.

Two people close to Sherlock do not make the mistake: Lestrade and Mycroft. Both are extremely perceptive about other humans, and both have known Sherlock for long enough to realize that Sherlock does not cleave to very many people. When he does find someone who inspires him to get both chatty and possessive, it isn't necessary to introduce sex to get Sherlock to display some very strange behavior. Mycroft probably knows he's not sharing a bed with John strictly for scary-Holmes-brain reasons; Lestrade might or might not even have bothered to develop an opinion on it. It's completely irrelevant: The existence of any relationship of emotional significance is enough to inspire change.

Why Sherlock doesn't correct people probably has a double handful of reasons behind it. (Sherlock is aware of it, no matter how much he ignores it -- he sees the humor when John makes a crack about people misinterpreting him hastily stripping off the jacket full of Semtex after Moriarty first leaves them alone, poolside.) He is for the most part uninterested in how people perceive him socially, and 'people think I'm gay and my flatmate is my boyfriend' is not something that would be a problem to his work often enough to bother with. He might be moved to correct someone at some point if homophobia were to present an annoying obstruction. He may find it useful in that when people are under that impression they refrain from making passes at him or asking why he isn't dating/hasn't settled down, which probably happens on occasion, and which he probably considers a tiresome waste of time.

He may just be pleased that he is somehow managing to get across, in whatever garbled way, the idea that he and John come as a matched set and are not to be separated. For all that he recognizes the danger inherent in letting it be known that he cares for someone to the point where he could be hurt by hurting someone else, Sherlock is surprisingly un-testy about the the realization that he cares at all. He openly and explicitly describes John as his friend, to himself, to John, and to outsiders; he feels no need to conceal or explain how it is that John has permission to follow him on cases, talk to him, question him, argue with him, or request (and receive) patient expansions of what is going on in Sherlock's head, when other people decidedly do not. The attachment is apparently categorized as a fact of life, like gravity; Sherlock is absolutely un-self-conscious about acting on it, and one gets the feeling that if he were asked to explain why he did a thing John asked him to, the answer would be delivered in the same impatient, patronizing tone as 'because things fall down when you drop them'.

(The most difficult bit about this for Sherlock actually seems to be figuring out how to get things out of his head and into language so that they can be correctly conveyed to his faithful blogger. John is good at reading, and Sherlock is accustomed to not caring; when the non-verbal process breaks down, as it does on occasion, Sherlock can get quite upset over suddenly being dumped back into the feeling of not being understood. This is the part Sherlock is having to learn, sort of exchanging with John tit for tat -- John gets lessons on the fine art of deduction whenever he asks, and Sherlock gets a much better picture of what parts of the inside of your skull need to be verbalized when dealing with someone you actually care about.)

Why John keeps correcting people is also easy. Sporadically I see people complain that having him continually tell everyone 'but I'm not gay' implies there's something wrong with the idea; given that John has no real opinion -- and that it has apparently not really crossed his mind that he'd need one -- about his sister being a lesbian, I rather doubt that. (Also, on a meta-level, because one of the writer-producers is both openly gay and responsible for some of the vast array of LGBT-friendly stuff in Doctor Who.) Partly it's annoying when other people persist in having an idea about you that happens to be wrong, but largely it's because this wrong idea leads them to interact with him differently than they would otherwise.

The relationship with Sherlock demands -- and John voluntarily gives -- a lot of love and loyalty, but so far as Sherlock is concerned it isn't sexual and doesn't demand fidelity. (Attention, yes; exclusive attention, no. Sherlock doesn't appear to care much about what John does when he's not looking for his flatmate, although he is somewhat childish about other people who might potentially prevent John from giving Sherlock his attention when Sherlock wants it.) The fact that other people think that it is and it does makes them assume that John would not be interested in certain types of relationships -- not just the 'romances with women' type, but also the 'random unattached guy' type, since with Sherlock around he's also perceived as settled down or taken.

Can't wait for series three. Sherlock is going to get both hugged to within an inch of his life and also punched in the face, but it's a toss-up as to what order that'll go in. I'm under the impression from a few of the press mentions that the last scene at the graveside was partly or wholly worked out by Martin Freeman between reading and rehearsals; if that's accurate, then even the amount of attention he's currently getting for being brilliant is not nearly enough.