The religious argument, spearheaded by the Catholic Church but also strongly supported by many other religious groups. These argue very simply that life begins at conception. An embryo is a fertilized egg, and therefore it is a life; embryo screening results necessarily in the destruction of embryos, and is therefore taking a life.
A further religious objection is that the selection of what children should or should not be born should be up to God, and people should not attempt to take a role in it.
There are many other groups concerned with the ethics of embryo screening. One of the most serious arguments is the concern that allowing embryo screening to progress to what seems its natural end will result in a global eugenics program, where prospective parents will be able to “shop” for the preferred embryo. The advocates of this argument believe that this will lead to “designer babies”, children born to fit a certain profile. And just as only the wealthy can afford designer clothes, this would result in a dramatic difference between the rich and the poor, as such on-demand screening is likely to be incredibly expensive. The rich, therefore, will end up with made-to-order babies, while the poor will be left to the natural order. In this situation, wealth will perpetuate wealth by breeding for it, and the low-income will become second-class citizens to a master class of tailor-made children.