What's interesting about a killer orangutan and a purloined letter? Or about the endlessly fascinating literature that grew from Edgar Allan Poe's valiant effort to push back against the madness trying to create an empire in his mind? This is a mystery with no solution. We know the facts, but we never fathom the explanation. It's not that we haven't tried.
Maybe, some arguments go, we read mysteries for psychological reasons. Perhaps figuring out the puzzle or enjoying the vicarious thrill of the search provides emotional satisfaction. Or maybe mysteries provide us with the childlike delight of a sequence of surprises, comparable, say, to a Charlie Chaplin routine followed by a topper and then a topper to the topper. In one psychoanalytic explanation by Dr. Charles Rycroft, the victims are parents, the criminals the readers' anger at parents, and the detectives, well the detectives discover they are looking at that anger in themselves. Maybe the authors and readers are all the characters in a story, with their detective side punishing their criminal side for crimes--impulses they have or actions they've taken. Such a detection and punishment symbolically cleanses their sins. This symbolic cleansing is so pleasurable and so chronically needed that we seek it over and over. Maybe Freud was right. We are discontented with our civilization, always struggling with our primitive instincts. On this interpretation, we are the criminals, and being caught provides the symbolic punishment we need to exorcise our guilt for the instincts.
Perhaps readers of mysteries fear uncontrollable social change and see in mysteries the gallant defense of the status quo. This social defense theory has become complicated by many characters like Edward G. Robinson's Rico or Tony Soprano who make audiences question their identification solely with the forces of law. Or consider Dexter, the serial killer who kills killers, and Vic Mackey of The Shield, who kept crossing the border between cop and criminal. These characters make audiences ponder the acceptable limits to controlling criminality.
Reading or watching mysteries provides a rehearsal for what might happen in our own social lives. Young girls watched Beverly Hills 90210 and its offspring to find models for their growing selves (a cringe-inducing fact for many parents) and experience situations that might occur in their lives before the incidents happened. So, too, mysteries prepare us for the crime we fear we might experience. Having read and seen enough examples, we have mentally rehearsed our various potential roles in any crime we might encounter.