Continuity mistake: Dexter kills Jimenez with a chainsaw and is wearing an apron. But he gets blood all over his shirt. He leaves in a hurry after getting a call from Rita about her door being unlocked and him having the only other key. When he shows up, there is no blood on the same shirt he was wearing.
Continuity mistake: When Dexter wakes up in front of Rita's house, he has a sweat patch on his shirt. When he gets into his car a minute later, it's gone.
Answer: Two reasons. First, as a cop he knows that there are lots of murderers walking around free due to flaws in the system so he uses Dexter's "urges" to right the wrongs in the system by taking out people who have no right to walk around free. Secondly, by taking him to a psychologist he runs the risk of having him committed and he doesn't want that for obvious reasons, so he figures it is best to channel his urges to what he considers a greater good.
The_Iceman
In addition to the earlier answer, in the last season (8th) of the show, we are introduced to Dr. Vogel, whom Harry had been discussing the situation with Dexter as well, and it is shown on-camera that Harry describes what Dexter has done (killing)... So, technically he did consult a psychologist/psychiatrist, just not having Dexter and her actually meet. But Dr. Vogel was aware of whom it was and how to intercede.