The common argument is: Darwin introduced the theory of evolution. This theory implies that a species will become stronger/faster/whatever if particularly strong/fast/whatever individuals are more successful in propogating. Thus, according to this theory, we should kill off/sterilize the weak to keep the species strong.
Actually, deliberately manipulating the gene pool is called artificial selection, and modest changes in a species (such as becoming stronger or smarter) are examples of what creationists would call microevolution. This specific form of evolution is particularly hard to dispute, and was understood and put into practical application in breeding domestic animals for a very long time before Darwin.
Darwin's insight was that natural processes influenced species in a somewhat similar way; the difference being, of course, that natural selection favours traits that contribute to survival and propogation of individuals, rather than suitability for humans. He first argued that natural selection would -- given enough time -- cause entirely new species to form; and that all life on Earth had come about this way.
So, in other words, Darwin added absolutely nothing to our understanding of heredity that would be of interest to a Nazi-style geneticist.