Not true. You left out thr part where Eugenics allows and encourages the Church (or the civil authorities) to deny certain people the right to marry anyone at all.Eugenics is not anti-Christian. It's saying nothing more than that the purpose of every marriage is divine ends, not the lusts of the individuals. And the Church has the ultimate right to sanction or not sanction a marriage. Just like it has the ability to refuse marriage of first-cousins.
Of course, if you deny lots of young men the right to marry and procreate, they are likely to become more aggressive and violent. So you will likely end up allowing and even encouraging then to use pornography, prostitution, and even undergo sterilization (which will be presented as a "voluntary choice").
And that's not to mention that "desirable" people would likely be encouraged to fornicate in order to have many babies, turning the babies over to the state once they are born. This happened in Nazi Germany, and in my opinion was a greater evil than the alleged Holocaust.
So the Church would be picking and choosing who can and can't receive the sacrament of marriage (and all the joy amd beauty that goes with it) and they would be doing so based on what traits they (not God) consider to be desirable in the creation of the next generation.
Eugenics is pure evil.