Continuity mistake: When Dex stabs Lila, the knife goes in near her stomach, where her vest starts. But in the close up shot, the knife is higher up in her, in her chest. (00:48:45)
Continuity mistake: In Paris, when Dexter grabs the knife off the table in the close-up, he's wearing the black glove on his right hand, but it cuts to the wide shot and both of Dexter's hands are bare; then in the next shot the black gloves reappear. It's rather odd that the actor was even filmed without wearing his gloves in the wide shot.
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.