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.
My assumptions and I stand corrected, and my decision to Elvis the TV stands reaffirmed!