Our Father - S3-E1
Continuity mistake: When Dexter gets out of the car and talks to his sister, the strap on the camera keeps flipping back and forth. (00:52:45)
Our Father - S3-E1
Continuity mistake: When Dexter and Vince are next to the dead girl, in the side shot, the tied string from her top is visible on her back and her hair is to the side. But in the overhead shot of her, her hair is covering the tied string and spread more over her back.
Our Father - S3-E1
Other mistake: When Debra is talking about her new haircut, she states that she has changed her hair "for the first time since she was 8." However in various flashbacks throughout the show she has drastically different hairstyles from her 'usual'.
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.