It's been proven by scientific study. A lot of abortions are done by lower class single mothers, whose children tend to grow up to be delinquents who then move into dangerous crime.
By removing this unwanted generation, we can create a safe and healthy society.
It's not quite that simple.
The big problem with eugenics has always been our lack of understanding of genetics coupled with the nature of the person capable of putting it into practice.
Genetics aren't a solved problem yet. That means, at best, we could kill millions and have a very minor effect on actual crime rates, and the nature of humans means you can't really isolate the genetics that are affecting such things.
This means that abortions being more common in one section of the population at one time, doesn't mean it'll stay there, and the cultural factors of the day, that'll change in responce, will also have effects.
In other words, it's going to be uncertain that removing a whole groups genetics will do anything specific, and abortion being common has many other cultural effects that might be worse. That'll only change when we truly understand our own genetics. It's likely to have some effect on crime rates, if it goes far enough, but..... There's been massive amounts of abortion in a number of nations, and crime rates don't seen to directly go with that...
Honestly needs more study, before I can speak with any real authority on that. I'm not sure about it, but it could well be true. However, next point is different.
Then there's the other big factor in eugenics. The kind of person who's willing and capable of putting them into practice is always going to be a monster, and they'll have to be a powerful enough monster to do so. Said monster is going to do things his way, and that's not likely to be up on the latest science. It's also going to be used more as a tool of control.
Honestly, if you're a monster, you might want to get rid of criminals, perhaps. But, you're also going to want to get rid of your rivals, and any group that might become a threat. That leads to Pol Pot, and a third of Cambodia getting killed, on the basis that they were educated.