Why the Nazis?
That won't stop the heinous folks at the Coral Ridge Ministries from spending a million bucks promoting the absurd link, but it's worth remembering why it's false. We can turn, as Nick Matzke has, to professional historians like Robert Richards, who recently wrote: "It can only be a tendentious and dogmatically driven assessment that would condemn Darwin for the crimes of the Nazis."
Or, like RSR, we could show how the particular linkages offered between Darwin and Hitler are tendentious, dogmatically driven, and plain wrong.
But there is a simpler way. The problem with these analyses is that there's nothing Darwin said that could have inspired a normative political philosophy. He observed how the world works, how A follows B. Whether it ought to in a given situation is entirely different, and Darwin didn't address those sorts of normative questions.
Hitler's horrific acts did not come from the idea that certain unfavorable traits could be removed from a population by selective breeding; that realization stretches back through thousands of years of human civilization. Darwin may have formalized the logic of it, but he did so by considering the accumulated wisdom of pigeon-fanciers, dog breeders and livestock producers. There was no secret in that regard which Darwin elucidated. Hitler's flaw lay not in recognizing an obvious truth about the world, but in identifying ethnic origin as an unfavorable trait, and in seeking to use the force of government to effect selection on that and other traits. The idea that natural selection ought to be government policy simply doesn't originate in Darwin. Darwin identified a natural process, a process that works all on its own.
Darwin did not produce a normative philosophy, he provided a descriptive and predictive theory. Newton did the same, as did Einstein. We cannot then claim that the normative philosophy of Nazism derived from Darwin's scientific work.
Some will claim that the normative portion, the part where certain groups were deemed lesser, comes not from the science, but from Darwin's rhetoric. Darwin does occasionally refer to racial groups in a way that suggests that some are superior to others. But in this regard, he was not innovating. He was a reflection of the biases of his day, biases which he was able to overcome. Indeed, if anything, a philosophy derived from Darwin is fundamentally egalitarian. As I said before:
Humans have evolved as long as fruit flies and bacteria. While apes are in decline worldwide, insects are ever more diverse and numerous. A phylogeny doesn't let you call one branch better than another. That's a radical egalitarianism, and it applies at all levels. You respect all people, and all life, because every being is a result of an incredible process, extended in time and space – a struggle against oblivion.That egalitarianism, the idea that all people, and all races, and all species, share some essential element, is fundamentally Darwinian, and is a powerful counterforce against genocide, as it was for Darwin against slavery.