He doesn't. He's had, for instance, two middle-aged teachers, a man and a woman. (There was a young woman there, too, a student of theirs, but don't be sick -- she was his granddaughter. Then she left.)

He's never had an actual child, or an elderly person, and the non-humans have usually been human in appearance, but he's had all sorts of companions. Including a tin dog.

As for why, in universe, it's that he really does need other people, whatever it may seem like, and out of universe -- well, in "The Deadly Assassin," the one episode without a companion, it was really, really, really awkward because he had no one to explain what is going on.