Common Descent
The biggest argument in "The Descent of Man, and Selection in Relation to Sex" is undoubtedly the concept that all humans are descendants of one common ancestor. This point of view was, in the racially charged period of the 18th century, rather controversial. While many had already accepted Darwin's theory of evolution, it took a few decades to connect the dots and allow humans to be included into the theory. Darwin, a fervent supporter of his own theory saw that intellectual discussion often moved towards spirituality when trying to explain the human descent. Horrified by this return to old concepts, he decided to publish a longer book on the descent of man than originally planned.
The Human Mind
One strong critique present at the time was that the difference between the human mental abilities and those of our closest relatives, the apes, seemed to be so vastly different that a natural evolution of this mental ability seemed illogical. Even Darwin's co-scientist of the evolution, Alfred Russel Wallace, was inclined to dismiss the theory for this point. This is why Darwin included a whole section on the evolution of human abilities into his second book. The book discusses similar traits, if of a lesser extent, in animals. He uses dogs and apes as examples to show that the basic structures of the human mind are present in animals and with the help of natural selection can be grown to the modern extent.
Human Races
Potentially the most controversial theme in Darwin's book is the discussion of races. Charles Darwin was a man of his time and while he clearly opposed the concept of slavery, he also considered certain populations to be inferior to others. Nevertheless, in line with his earlier theory of evolution, he wanted to show how different races can develop from one common ancestor, through natural selection for their habitat. He also discussed that humans are divided into races and not species by showing that sexual relations between races result in viable children.
Sexual Selection
The concept of sexual selection was, prior to the publication of this book, used as the biggest critique for Darwin's theory of evolution. If evolution favors those traits that help the species survive, why are there birds with huge plumage that decrease their fitness, or deer with antlers that make their life harder? In the second part of the book Darwin discusses this by introducing the concept of sexual selection. Animals develop certain traits through evolution as they make them more interesting to the other sex. This addition to the original theory explained those critical points mentioned above. It also explained why many species show a clear physical difference between male and female specimen.
Social Darwinism
This element of the book, while only called Social Darwinism after the death of Darwin, is probably the most difficult to discuss. In his discussion of the human races, Darwin argued that some genetic superiority allowed the European cultures to become the beacon of society. This superiority, in Darwin's words, also would, in the near future, either incorporate or wipe out the so called savage races. He also stated that the civilized cultures, through their superior moral, allow weaker individuals to propagate which technically weakens the whole race. Unfortunately, this argument has been used throughout history to justify racial cleansings and genocide, resulting in such horrible historical facts like the German Third Reich. While Darwin's argument was that the Western morality should stop this, his opinion about other cultures marks him as a privileged child of his time.