As cloning didn't exist in the Victorian era, we know for certain that Sherlock Holmes was fathered by a male of the species. But did he grow up with a father?
Mycroft Holmes, the elder brother choosing government service, seems like the sort of fellow who is following in the family footsteps. Mycroft was famous for lacking the energy to pursue a path outside of his routines, and in picking a career, he seems like the sort that would take the path of least resistance: "Father worked for the government, so I shall as well."
Younger brother Sherlock, however, is creating his own path, and it's a path that no one before him ever walked. It's a path so outside-the-box that it's hard to imagine a present father figure not raising a major fuss, or at least some serious recurring questions, about every step Sherlock took.
Add that to the fact that when his best friend's father makes a random comment about Sherlock's potential as a detective, Sherlock takes it to heart, just the way a college-age youth without an actual father in his life might do. He's looking for something. And that something he's looking for reveals a void in his life.
Many a writer has seen this in Holmes and given him a father that shunned him, a father removed from the family by his own crimes, or just one who died. BBC Sherlock is quite the exception in giving Sherlock Holmes perfectly normal parents and a father who has been in his life all along . . . yet still seems to have nothing to do with Sherlock's evolution as a detective.
It might be something of a writer's challenge to create a father for Sherlock Holmes who both inspires and guides his son into what was a completely novel path at that time and somehow is not worth ever being mentioned to Holmes's closest friend. Yet I have a feeling that someone will get there someday . . . enough people are certainly trying out every potential Holmes these days. It might even have been done already and I'm just not aware.
I hope such a version of Holmes's backstory does exist, because we'd like for him to get a few more happy Father's Days than he gets currently.