I've just finished watching the first two seasons. Dexter's character seems very inconsistent -
On one hand, he's supposed to be the classic psychopath, completely devoid of feelings/emotions himself and incapable of understanding other people's feelings (as is evident from his conversations with everyone). This leads to him having to pretend all the time to look normal and even start a fake relationship with Rita just so that he looks to be leading a normal mundane life to others.
But then, on the other hand, he cares way too much for Rita and the kids. Goes to great lengths to not having to breakup, impulsively picks fight with Paul to protect Rita (against his code and common sense), makes big efforts to keep Rita/kids out of harms way. He stays with her or keeps trying to get her back in his life even when it would be more logical to go with the flow and find another normal (unlike Lila) girlfriend to keep up the appearance of a normal life. And its worth noting that Rita brings absolutely no real value to his life other than the happiness derived from his emotional attachment to her family.
Why this dichotomous behavior? Is he a psychopath or not? Why so obsessed over Rita?