Selective breeding happened in other parts of the world but mostly with mammals. I know nothing about anthropology so I'll take a Socratic stab at the question.
I think it takes a aquaculturist point of view -- you have to have folks whose livelihood depends on the animal they are breeding and those animals have to be completely domesticated. If wild stock are plentiful then you don't need to domesticate.
Did these conditions exist elsewhere for the common carp? I dunno but it seems likely that they did not -- I know of no other place where the carp was purposely raised as a food animal nor of a people who were so dependent on it. Then again, I know jack squat about agricultural anthropology so I could be wrong.

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