In the first paragraph of the story, the narrator says that he doesn't want to "write a treatise" (i.e., an essay) about his suggestion that reason is always the better for a little imagination, and vice versa. "The Murders in the Rue Morgue" reads like an essay anyway, even though most essays dispense with murderous monkeys. The narrator and the protagonist spend a lot of time showing what kinds of intelligence are valuable, and what kinds are not (sorry, chief of police). And the narrator sets up the case of the murders in the Rue Morgue as proof that superior reasoning allows the human mind to make guesses at stuff beyond its knowledge, and then back it up with cold, hard evidence.
Dupin distinguishes himself from the police because, while they are both analytical and cunning in their way, Dupin has the imagination to think outside of conventional assumptions.
Dupin's genius for observation is incompatible with social interaction: he uses human emotion as evidence in his chains of reasoning rather than as a means for bonding with others.
When we think "detective story," we think of something like Law and Order: SVU or The Mentalist or Cold Case, where the point is to put together all the clues to catch the perpetrator before he can kill again. Those stories are all about judgment. Society can't tolerate a killer in its midst, so we have the police (or the psychic, or the medical examiner, depending on the franchise) track down evildoers.
We don't know if it's because Poe wrote the first detective story or what, but "The Murders in the Rue Morgue" isn't really like that. By choosing a non-human killer, Poe neatly sidesteps the question of "justice" (because an Ourang-Outang isn't going to learn any better). And Dupin himself is not particularly interested in figuring out the case until a gentleman's obligation comes into it. In other words, he has his own code of honor, but he's not doing this for abstract reasons like protecting society or upholding the law. Neutralizing the question of justice gives Poe more of a license to turn his story into a puzzle. There's no strictly moral lesson to be learned here, unless it's that creativity is good and leaving your windows open and lights on at 3am is bad.
Dupin's decision to take on the case to repay a favor from Le Bon shows that he believes more strongly in honor than in justice.
By making the killer of "The Murders in the Rue Morgue" an ape, Poe shifts the task of the detective away from moral judgment and towards pure logic.
The narrator of "The Murders in the Rue Morgue" is a stranger in a strange land, a man of unknown nationality visiting Paris. While he and Dupin are bonded, he nevertheless often describes Dupin specifically as a Frenchman. The testimony with regard to the murder case arising from the neighbors in the Quartier St. Roch is similarly nationally marked. There's a bunch of French, English, Italian, and Dutch people, all presumably sharing a neighborhood. While Paris is the capital of France, it also comes across, in this story, as the capital of the world, with all kinds of people living side by side. There's no sense of rootedness or unified national culture to be found in the midst of this thriving urban setting.
In such a dense city space, you expect misunderstandings to come up. And they do, literally. None of the witnesses can agree on the language that they hear spoken over their heads as they race into the house in the Rue Morgue, but they all think it's a foreign language. In a neighborhood in which many nationalities of people exist cheek by jowl, there's still one boundary that's maintained absolutely: the animal remains foreign. In other words, whatever his or her nation of origin, everyone in Paris is connected by their common status as reasoning, rational human beings. What needs to be excluded to keep up this status quo is the irrational emotionalism of the Ourang-Outang.
"The Murders in the Rue Morgue" depends on the diversity of modern city life to make its story of a murderous Ourang-Outang plausible.
Dupin's coldness and calculation exclude him from society as much as the Ourang-Outang's extreme emotions do.
The narrator of "The Murders in the Rue Morgue" is upfront about his own personal tastes, and when we say upfront, we mean it literally. He spends the first several paragraphs of his story expressing his admiration for certain kinds of thinking, which he finds in his pal Dupin. We sit back and watch him express his awe at the man's genius the first few times and we think that he's justifying why he has selected Dupin as the protagonist of his story. Fair enough. And when he spends whole pages on one chain of reasoning from a fruit-seller to Chantilly the actor, we think, well, maybe this is getting a bit heavy with the hero worship, but we can deal. But as the story goes on and the narrator meets every new thing Dupin says with "mute astonishment" or "this is beyond my comprehension," we start to wonder why expressions of amazement are so important to this story.
There are a couple of things that this "awe" might be doing. First, the narrator's astonishment gives a plot-level reason for why Dupin needs to talk through his solutions carefully and slowly. Second, it signals to we, the readers, that we're supposed to be similarly in awe of what Dupin is doing. And third, it increases the suspense. The gap between the narrator's understanding and Dupin's keeps us on edge, as we wonder what Dupin knows that the narrator does not know.
The narrator's constant praise of Dupin's uncommon genius reminds the reader to imitate his methods of thinking to solve the puzzle of the story.
The narrator's awe-struck responses to Dupin slow down the dénouement and step up the suspense of the narrative.