Which naturally leads to this sort of thinking: [Eugenics]
No, it doesn't: eugenics is the belief that some human races are superior to others, which is fallacious. Natural selection is simply selection based upon those who just so happen to survive long enough to reproduce. Those with beneficial mutations are more likely to reproduce, so novel beneficial mutations become the norm in the long run. This is the theory of evolution and leads directly to the theory of common descent.
Eugenics, however, replaces natural selection with artificial selection, and is the mass extinction of entire races, even though there is no 'fitter' or 'superior' race: we are all as good at reproducing as each other. That is why eugenics is fundamentally flawed.
Evolution is about the survival of the fittest.
Christianity is about the redemption of the unfit.
Strawman and equivocation. "Survival of the fittest" is an inaccurate caricature, and the "fittest" and "unfit" do not refer to the same thing (the former best refers to genes that are more likely to be proliferated, the latter to humans in need of spiritual salvation).
While abuses occur within the Christian Church its core belief system does not support them. The same cannot be said for The Theory of Evolution whose core belief system treats as natural the extinction of the “unfit”.
If it occurs by natural means, yes. Otherwise one can hardly call NATURAL the extinction of a species by NATURAL selection.
These may be anyone who is politically out of favor as were the Jews in Germany where Hitler used “evolutionary” rhetoric to plead his cause.
Even though you're wrong, there's a very important question here: so what? The truth of common descent doesn't depend on how good said truth makes us feel. Astronomy is a humbling science, but it isn't any less true because of it. We may
want to be the centre of the universe, we may
want to be ultimately unrelated to the other animals, but reality rarely bends to the wishes of the masses: it is what it is, regardless of the consequences to humanity.