After Dunya's declaration that she could never love him, Svidrigailov realized that he needed more than sensual pleasure; he also needed human warmth and affection. His entire life was based on the theory that he was completely self-sufficient and self-contained, that he needed no one, that whatever he wanted he would simply take and ignore any consequences, and that his will was stronger than anything else.
Suddenly with his realization that he needed but could not will the human warmth Dunya could supply, he saw the failure and sham of his previous existence. With this insight, he simply cannot return to his previous mode of existence, which he realized to be false. Likewise, he cannot change. The only thing he has not willed so far is his own death. Immediately after these realizations, he has the dream about the little girl he picked up and who, under his touch, turns into a shameless whore. Thus, these realizations lead him to his suicide. Svidrigailov feels there is no other choice for him except to will his own death.
Svidrigailov's suicide is part of Dostoevsky's thesis that no man can set himself apart from humanity. There can be no superman, no Ubermensch, who is allowed to transgress the law. Sooner or later, every person needs human warmth and companionship.
