You have to wonder what the backstory is to this one. I mean, people who know and love Sherlock are absolutely, 100% convinced that John is Sherlock’s date the moment they see Sherlock and John together. It’s a running gag, obviously, but it wants explaining.
Sherlock is clearly a loner. He knows people (quite a lot of people, actually, more people than John appears to know), but he doesn’t choose to spend his time with any of them. He just solves puzzles. That’s all. He doesn’t enjoy the company of other people. He doesn’t go out for dinner with anyone, ever. (That point ever-so-nicely underscored by his bewildered question to Irene in Scandal.)
It’s pretty apparent to us by now that Sherlock isn’t particularly moved by attractive women. He doesn’t particularly react to Irene at all, even when she’s propositioning him. Maybe others have seen that in him too; he doesn’t seem interested. So they may make the next logical step (“Oh, he must be gay, that’s fine.”) even though he isn’t particularly moved by men, either.
Maybe Angelo told Sherlock ages ago that he was always welcome in the restaurant, any time, with anyone he likes (“Bring a date! It’s on the house!”), and Sherlock never turned up. Then one day, months and months later, he appears with a fellow he’s clearly fond of. Sherlock must be fond of this bloke, he must be trying to impress him, right? Because he’s willing to spend an evening over dinner with him, an event which Angelo has never witnessed. He’s willing to sit in a restaurant like a normal person with this fellow, so he must be tremendously special to Sherlock.
Sherlock doesn’t have friends. So maybe no one jumps to the conclusion that Sherlock has just made a new friend, because…well, he could have been friends with dozens of people but chose not to be. Mrs Hudson loves him, Molly loves him, Angelo loves him, Lestrade loves him too: there must be others, people he’s helped and rescued along the way, people who respect his brain even if they think he’s entirely too odd for this world. I’m sure there are a number of people who would be more than happy to sit across a table from Sherlock if he ever felt lonely. But he never takes anyone up on that. People who admire him are just a side effect of his work. He doesn’t solve the cases for them and their reactions. They’re an unintended but not entirely unpleasant side effect. He doesn’t appear to give them much thought at all. He ignores them.
For some reason, Sherlock takes to John almost immediately, and goes about trying to impress him. Everyone around him notices that: Mycroft asks about a happy announcement, Mrs Hudson makes her assumptions, as does Angelo. Sherlock is the observant one, but everyone around him sees that John is special to him. John doesn’t feel particularly special yet, because he doesn’t know Sherlock. He doesn’t know that Sherlock has just made every possible exception for him.
Sherlock doesn’t take John to Angelo’s in order to work on the case. He takes John there to trick him into losing the limp. Sherlock takes John out for dinner to cure him.
There are three explanations I can think of for that behaviour, all of which I think are true.
The first is that it’s another curious puzzle for Sherlock to solve while waiting for the next break in his current case. (“Can I cure a psychosomatic limp? I bet I can.”)
The second is that John will make a better addition to Sherlock’s life minus the limp (there are, after all, seventeen steps up to 221b, and he doesn’t want to give up his bedroom on the first level). It would be better if John isn’t struggling up and down stairs. Sherlock is not a patient man. I’d say that Sherlock realizes that John would be more of a help on cases minus the limp, but I don’t think Sherlock realizes yet just how critical John will become to that enterprise. (This is, after all, before John turns the tables and impresses the pants off of Sherlock by shooting a cab driver through a window.) If he did realize it, I’m sure he’d have cured that limp long before dinner time.
The third explanation for Sherlock’s act of kindness is this: “You’ll be impressed with me if I can cure you.” The distance Sherlock is willing to go to impress John is kind of epic, when you think about it. It doesn’t look epic to John at the time, but if he ever considered Sherlock’s behaviour after the fact, from the vantage point of knowing him for a year or more, he must marvel at it a bit. Sherlock took a complete stranger to dinner. That’s unheard of. Sherlock takes a very special and unusual interest in John immediately.
No wonder Angelo thinks they have a romantic connection. This is Sherlock pulling out all the stops. It must be love.