(I think some sci-fi story had cute robot kids causing the extinction of the human species, but I forget which one this was.)

I read a story where prospective parents had to first take care of a robot baby for training, but it was so awful that many decided to just not have children ... resulting in the demographic decline of America, and Chinese supremacy (the Chinese had designed the robot with that result in mind). It may or may not be the one you were thinking of.