Raskolnikov's reasoning for his crime is influenced by a theory he has formulated. In an essay he writes, he argues that humanity is divided into two categories: ordinary people and extraordinary individuals, or supermen. While regular people must adhere to the law, "supermen"—who are rare at any time—are entitled to defy existing laws and establish their own. Raskolnikov cites the French leader Napoleon as the quintessential example of a superman. He claims that Napoleon attained power by surpassing the laws that apply to common people, formulating his own rules, and accomplishing his objectives through wars that led to massive casualties. Since Napoleon was a genius, Raskolnikov believes he was celebrated as a hero rather than a criminal. Early in Crime and Punishment, Raskolnikov becomes obsessed with the notion that he is a "superman." As a result, he feels he is exempt from the laws that apply to ordinary individuals. (In the original Russian text, Dostoyevsky frequently uses a term meaning "overstepping" or "stepping over"—essentially, transgressing. This term is closely linked to the Russian word for "crime" (prestuplenie). Raskolnikov chooses to murder the pawnbroker Alyona Ivanovna partly to prove he is a superman. However, his persistent doubt and confusion throughout the novel reveal that he is not a superman. Through the story, Dostoyevsky aims to illustrate that the idea of a superman is an illusion. Dostoyevsky argues that every human life is precious, and no one has the right to take it.

Dostoyevsky's depiction of the superman theory through Raskolnikov anticipates the concepts later developed by German philosopher Friedrich Nietzsche in the 1880s. For Nietzsche, the superman and his "will to power" represented the highest ideals. He believed Christianity hindered the superman and criticized it as a "slave morality." Dostoyevsky's view of the superman fundamentally contrasts with Nietzsche's. According to Dostoyevsky, embracing the "superman" theory inevitably results in death, destruction, chaos, and suffering. Instead of seeing Christianity as a "slave mentality," Dostoyevsky regards it as the true comprehension of humanity's role in the world and its connection with God. In Dostoyevsky's perspective, every person is valued in the eyes of God.