Just the threat applied today of the government taking away your children unless you can provide a minimum standard for them, is enough to convince many people to not procreate. Ie eugenics with a different process.
If you read the above paragraph and think "what's wrong with that", then you're in company with a lot of people who are not unreasonable. But it springs from the same idea as eugenics. Now consider the above paragraph applied to minorities or the indigenous population. Suddenly it is an awful thing.
You can also argue that nobody should have the right to pass on hereditary diseases and conditions to a child. What do you do if they want to do it anyway? Etc, etc. There are arguments for and against. Well being of the child vs human rights of the parent.
Edit: Down vote as much as you want. Eugenics is the above. Doesn't mean I'm for or against it. It was promoted at the time as a way of protecting children from growing up with "unfit" parents.