You can get married. There is an Orphanage in-game. Yet you can't make the "magic" or adopt. Ohh the sad sad day when the world realizes the Dragonborn is infertile/neutered (depending on race) and lacks the god given dignity to adopt a child :shrug:

If they didn't take the time to make sure there were potential spouses of each race and gender this is far beyond the effort that would have taken. The game's time scale is too slow for children to make sense too. Adoption perhaps, but that would be a complicated mess for AI I'd imagine.