Eugenics is technically sound science. Selective breeding for traits is something we do with plants and animals. It works. You want pug nosed humans that yield 20% more crops, you can breed for that . There is nothing about selective breeding that technically wouldn't work for humans.
Now. Despite all of that, we should not do it. It is a moral wrong. It would require us to violate the autonomy of people. Don't want short people, you can't let short people reproduce. And so on. That's what makes it icky.
That's why we don't do it. And why we shouldn't. Not because it wouldn't work, it would. But because it would require us to violate another's autonomy.
Eugenics isn't just selective breeding, it's the extension of genetics to traits such as "intelligence" or "criminality." These sorts of things are broadly non-hereditary.
That is exactly what the parent meant: Intelligence has in fact been shown to be hereditary to about 2/3rds. This is difficult to integrate into a humanistic world-view, so the easy way out is to outright deny that fact.