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.