Revealing mistake: When Dexter is retrieving a blood sample after cutting Benny Gomez's cheek, there is no blood in the dropper and he puts no blood on the actual slide. (00:49:50)
Revealing mistake: When Rita confronts Dexter about his accident being more than minor Rita turns the buggy with the baby in around to leave and it is clear the baby is fake. (00:38:20)
Revealing mistake: When Deb is texting "Looks like it" to Anton, the buttons she presses on the keypad do not correlate with the message itself and the phone doesn't show any auto-correct feature being utilized, indicating that the text message was added in post production.
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.