Disclaimer: nothing mine. I apologize if Dad and Mummy Holmes were given a name in BBC canon. I didn't catch it and invented them.
Learning to fly (requires falling)
It all started the day that there were no babysitters available. Or perhaps it started much before, when a young girl was reading Asimov. The woman who'd later become the institution known as Mummy Holmes loved maths, and she loved the Foundation cycle.
When years later she decided that she'd endeavour to become Hari Seldon (because the principles of psychohistory should work), she wasn't committed. She was just brilliant enough that people suspected she might succeed, so she was given a place in a government founded research centre who held many more of what ordinary people would call would call mad scientists but that the bureaucrats considered people who might just change the world.
Then came the day when Siger Holmes just had to help a friend in need and hence couldn't take care of Mycroft, and they could find no babysitter. So, against all regulations – but what damage could a seven years old child do? - Mummy Holmes brought him to work with her. And there they met.
Mycroft, who decided to sneak around in search of something interesting while Mummy was completely absorbed in her numbers, found the little thing beyond a heavy glass. On the door by that window was written SL47.
It was a baby. A perfect baby, if you asked him, with eyes the most beautifully puzzling shade of blue that Mycroft had ever seen. He was tiny, and had more angles in his body that Mycroft had ever seen in a baby of that age – they were mostly screaming little balls. And he had the softest-looking, fluttery, feathery wings that ever graced a baby bird, but they seemed to fit him very much.
Not that this one wasn't wailing too, like every boy his age seemed to do. Nobody was fussing over him or running to see what the problem was, though, and that was just sad. Mycroft slipped in the room and apparently all the baby wanted was company, or maybe to be tickled, because holding him, tickling him and running reverent hands down down his feathers was all Mycroft did, and the little one was giggling in no time at all. Mycroft parted from him reluctantly, later, but it was time for his afternoon snack and Mummy might notice his absence.
That evening, at dinner, he shocked his parents saying, "You think that I'm lonely. Well, maybe I am. A little. You're thinking about trying for another child. Don't bother. SL47 would do perfectly as a little brother."
"Mike, you shouldn't even know about him," Mummy replied sharply.
"Well, clearly I do. Don't worry, I've not hurt him. I wouldn't," the boy protested vehemently.
"I've not said so, Mikey. Of course I know that. But I can't just bring him home, either. He's propriety of the British government," she tried to explain.
"Well, he didn't seem to care very much for him. He was left to cry. And who is the British government, anyway?" Mycroft asked, already plotting how to convince him. He was good at having people do what he wanted.
"It's complicated," Mummy answered, very unsatisfactorily. And it was left at that.
Until, four years later, when he'd resigned himself to being forever alone in a world of goldfishes, Mycroft got his wish.
Despite the hollow bones and the wings SL47 refused to fly – to levitate, even – which should, according to his creators' theories, have developed together with walking. But it hadn't, and they were tired of waiting and raising someone who would, at best, be fit for a freak show.
They decided to scrap the experiment, though they didn't kill him themselves – nobody on the SL team had the stomach for that. It turned out that nobody at all was ruthless enough for that, and so , with the semi-consent of some people and keeping others carefully unaware, Violet Holmes ensured that Mycroft obtained what he wanted, a few documents were forged and SL47 became officially Sherlock Holmes.
A little boy with a huge secret ("Never, ever, ever let anyone glimpse your wings, Sher; they'll take you away!"), an enthusiastic if overprotective older brother ("Finally someone to play Deductions with!"), and loving parents ("You're absolutely perfect the way you are, love." "But I can't fly!" "Well, neither can I," Siger smiled).
And psychic classmates, going by the number of freak he received despite carefully hiding his...malformation. He never objected against them because that was, you know, true.
"They don't know a thing, Sher, don't worry. They're too idiot to have noticed. They're just envious of you. But believe me, they don't matter."
"I know that, Mycroft," he huffed. Still, he dreamed of becoming a pirate and having mates to have adventures with. For now, Readbeard would have to do.