Factual error: When Dexter is reading the list of drugs found in the autopsy of the murder victim, one listed is "Cialopram." This is a misspelling of the antidepressant Citalopram; misspellings do not occur on drugs lists in toxicology reports, as they are computer-generated. (00:37:10)
Continuity mistake: When leaving his home at the end of the episode, he locks the door, then sees a big storm and walks back inside without ever unlocking the door. (00:49:30 - 00:49:52)
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.