What little I know about this show is based exclusively on this article...my supposition is that the character is driven to his acts because of what he's seen at crime scenes as the result of his work. Admittedly an assumption, and probably a poor one to make. Having said all that, if the themes of the show are what I suspect, they are really nothing new:
Shakespeare & The Law: Obligation, Vengeance, and the Abuse of Power
Good guess, but I think wrong. There are flashbacks to his life as a kid. His father was a detective. Dexter started acting on urges as a child to kill and hurt animals. The father picked up on this, and, knowing there was no way to fix it, tried to channel it by teaching him how to find bad people and kill them without being caught. Kind of like a serial-killing superhero.