It probably started out with Sherlock pretending to have an imaginary friend who he made into his sibling to explain why his imaginary friend is ALWAYS by his side/in the house/on family trips.
Mycroft indulged in Sherlock's play sibling to the point where he tripped from reality into fantasy and he also started to believe it.
OR Mycroft had an imaginary sibling and when Sherlock was born, Sherlock grew up believing it.
They got older and grew out of it but they made up a story about what happened to the sibling ("you know what happened to the other one") to explain/cope with the loss of imaginary sibling.
The third Holmes sibling was a figment of Sherlock and Mycroft's imagination
Mycroft indulged in Sherlock's play sibling to the point where he tripped from reality into fantasy and he also started to believe it.
OR Mycroft had an imaginary sibling and when Sherlock was born, Sherlock grew up believing it.
They got older and grew out of it but they made up a story about what happened to the sibling ("you know what happened to the other one") to explain/cope with the loss of imaginary sibling.