This novel is anti-social through the key theme of alienation, which is summed up in the character of Raskolnikov and his actions. Note how he himself is separated from society at the very beginning of the novel, where his pride is what he believes makes him different and superior to everybody else, and unable to relate meaningfully to them. His own view of life places himself as the most important individual on the planet, and thus everybody else are free to be used by him. Note how he shows himself to be anti-social in Part II Chapter 1, after he has committed murder:
What was taking place in him was totally unfamiliar, new, sudden, never before experienced. Not that he understood it, but he sensed clearly, with all the power of sensation, that it was no longer possible for him to address these people in the police station, not only with heartfelt effusions, as he had just done, but in any way at all, and had they been his own brothers and sisters, and not police lieutenants, there would still have been no point in this addressing them, in whatever circumstances of life.
Raskolnikov feels that now he has committed murder, he is different from everybody else around him; so different in fact, that it is unnecessary for him to communicate to others, and indeed it is not only unnecessary, but futile. He believes so strongly that committing the act of murder has propelled him into being a kind of "superman" in Nietzschean terms that he is so far above every other human.
This alienation is only something that increases during the novel because of his massive guilt and the delirious state that he enters. His inability to relate with those around him does him no good, as even those who seek to help and support him he rejects, such as Sonya and Dunya. The novel is a gradual progression of self-imposed alienation from society that only ends in the Epilogue when he experiences something of an epiphany as he learns that Sonya loves him. It is this that finally allows Raskolnikov to conquer his pride and selfishness and to metaphorically rejoin society.