What you are refering to is called Eugenics.
Eugenics is a slippery slope. Once the government starts telling certain people that they are not allowed to reproduce, then there is nothing to stop them from placing that same restriction on other unwanted groups as well. The issue becomes that the group in power can (and has) wiped out other groups that, for one reason or another, it doesn't like.
The Eugenics movement began shortly after Darwin's Origin of Species was released and over the following decades major governments sterilized, or even euthanized, the unwanted or unnecessary elements of their societies (60,000 mentally ill patients were sterilized without consent in the US alone). The existing eugenics policy (in the early 20th Century) in Germany was used as the justification to expand the system into a country-wide program of cleansing in an effort to purify the undesired traits from the 'master race', this program led to the annihilation of millions of Jews, Blacks, Catholics, Mentally ill (down syndrome, schizophrenia, retardation, etc), Gypsies, and political troublemakers in what would eventually be called 'The Holocaust'.
That is why we cannot allow selective breeding of the human race; because once it starts, nobody can know where it will end.