For the benefit of readers who don’t know what this is about:
Female Nidoran and Nidorina can breed with male Pokémon from the Monster or Field egg groups and lay eggs which will hatch into Nidoran of either gender. This makes sense. Male Nidoran, Nidorino and Nidoking can breed with female Pokémon from the Monster or Field egg groups, who will then lay eggs which will hatch into Pokémon of the mother’s species. This also makes sense.
What makes no sense at all is that Nidoqueen are sterile.
EDIT: I was mistaken; I think I had several Bulbapedia articles open at once and looked at the wrong one at some point. Nidorina can’t breed either; only female Nidoran can. This is actually what I *thought* was the case originally, until I decided to check my facts and then misread the reference. Oh, the irony. Anyway, this makes all of my speculation below much less plausible and I have no longer have any sensible explanation. Game Freak are just silly.
Adult Nidoqueen cannot breed at all. No, not even with a Ditto. As far as I can tell, this is merely one of the stupider oversights that Game Freak haven’t quite gotten around to fixing yet for some reason. I couldn’t tell you why; someone probably made a mistake in the original coding when they did Gold and Silver (given Nidoqueen’s unusual gender status, it’s not unbelievable that they could slip up with her) and it’s been copied and pasted ever since. Strange that they didn’t fix it when they overhauled the entire game engine for Ruby and Sapphire, but perhaps they hadn’t noticed it by that point. Hmm.
Anyway, there is actually a perfectly reasonable in-universe explanation they could use if they wanted to. There’s a conjecture in anthropology, which has been floating around for a while now and has never gained a whole lot of support but never quite seems to die either, called the grandmother hypothesis. Basically, the idea is that human women are able to live well beyond reproductive age because having older women around to help care for the children presents a tangible benefit to the survival of the community. It’s a common sense explanation for the phenomena of menopause and post-menopausal longevity, but it’s very difficult to prove scientifically (you can read more about the hypothesis in P.S. Kim et al., “Increased longevity evolves from grandmothering,” Proc. R. Soc. B. 2012). If you wanted a good reason for Nidoqueen to be unable to breed, this would be a solid place to start: Nidorina are the breeding adults, while Nidoqueen are the ‘grandmothers’ who hang around to help their daughters raise their own children and protect the whole group. This makes a great deal of sense considering that very few Nidorina would ever make it that far – they evolve using Moon Stones, so in the wild you’d expect to see one, perhaps two Nidoqueen in an entire herd. They have a more complex social function than just continuing to reproduce.