While genetic research has huge potential in early diagnoses, and possible prevention, of illnesses caused by genetic defects, the statement that one can determine (general) intelligence of a potential offspring by checking embryos seems nonsensical from the get go.
First of all would be the definition of (general) intelligence. What exactly is it? Even when assuming that an IQ test cannot be cheated, the concept of reflecting one’s general problem solving skills by a number makes little sense. Can we really say that a savant that heavily struggles with everything but in one field has the same intelligence as someone that is completely standard in any way when both have the same IQ score? I would say not, as the former would need much more support than the latter.
Furthermore, often points concerning something related to eugenics ignore the nature vs nurture debate. How much of our skills are dependent on our environment? To what extent can we say that our minds have a limit on how intelligent we are? It’s hard to say, as there isn’t much research about it, and experiments on that topic are often inhumane, historically speaking. So we need to keep this lack of knowledge in mind when talking about topics like eugenics.