Trivia: (POSSIBLE SPOILER) When Masuka brings up the list of doctors authorized to get the M99, Dexter removes his alias note that Dexter's fake alias (used to get the M99 tranquilizer) is Dr. Patrick Bateman. Patrick Bateman is the lead character of "American Psycho". This was most likely an intentional "easter egg" of sorts within the show.
Trivia: Michael C. Hall and Jennifer Carpenter, who play siblings on the show, were actually married in real life, from 2008 - 2011.
Trivia: When Dexter is looking at Isaak Sirko's file on his laptop, the top picture on the column of three is a screenshot of Ray Stevenson in Punisher: War Zone. (00:23:58)
Trivia: In this show, Christian Camargo plays Dexter's older brother. In real life, Michael C. Hall is 5 months older than Camargo.
Trivia: When Deb is telling Dexter that she has a date with Lundy that night, she remarks that he is 20 years older than her. In real life, Keith Carradine is 31 years older than Jennifer Carpenter. (00:22:30)
Trivia: John Lithgow revealed in an interview with GQ that he initially turned down the role of Arthur Mitchell, a.k.a. the Trinity Killer. He was convinced to change his mind by his agent and his lawyer. He ended up winning an Emmy for the role, so he definitely made the right choice.
Trivia: Some notable differences between season 1 and "Darkly Dreaming Dexter" - the first novel in the series of books that the show is based on - are that Deb and LaGuerta both discover Dexter's secret by the end, which doesn't occur in the show until seasons 6 and 7, respectively. LaGuerta is also killed by Brian, a.k.a. the Ice Truck Killer, whose true identity isn't revealed until the last chapter, and he is also referred to as the Tamiami Slasher. He also escapes at the end of the novel.
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.