No its not eugenics. Its keeping unsafe people from harming others. I didn't say they can't breed. Pretty telling statement from you that you went there first. You cannot teach empathy if the person doesn't have it naturally. That is just plain stupid. You can of course teach them to lie about it. It will be imperfect and they will only use it to manipulate people.
Most psychopaths are productive non violent and non victimizing citizens. Its apples and oranges. Many doctors have clear psychopathic tendencies. It doesn't make them pedo rapists or abusive. Like a clear lack of empathy does. It doesn't cause them to play games with peoples emotions for nothing more than their own entertainment. The two are nothing alike and like all human mental conditions there is some overlap.
The lack of empathy mostly overlaps with a cluster B diagnosis. Particularly NPD. Those are the people who say empathy isn't real or its learned.