Comic books have been something that I have enjoyed ever since I was a little kid. My grandfather first introduced me to Superman when I was about two or three years old, and that led me to other heroes like Spider-Man, Green Lantern, the X-Men, and especially Batman. Batman was and still is, my favorite comic book superhero of all time. His status as an icon is also burned into our cultural zeitgeist, but Batman isn't just your typical superhero. He's damaged, obsessive, paranoid, and his rogues' gallery is filled with criminals whose crimes are much crueler and darker than the crimes of villains like Lex Luthor, or Weather Wizard from the Flash.
However, Batman's most defining trait is his major and permanent psychological damage. Let's face it, Batman is insane, albeit mildly insane, but even then, that sets him apart from his Justice League compatriots in a defining way. The tragedy of Bruce Wayne's youth damaged and changed his psyche to make him what we know him as today.
Batman's whole motivation as a hero is revenge; he's looking to avenge his parents. Every criminal encounter he stops is symbolic. He feels like he's saving his parents again and again. It's an intriguing obsessive-compulsive behavior that Batman can't stop on his own.
He also takes on an entirely different personality when he's got the cowl on. Bruce Wayne is the true mask that he wears, but Batman isn't his true face either. The true face of Batman is still the afflicted youth that has lost his parents. Batman is an identity he adopts to escape that trauma and make him feel like he's correcting the wrongs of the past. It makes him feel like he's capable of stopping another situation of death, which he is indeed perfectly capable of doing.
Batman is also incredibly paranoid. He's hatched plans to contain and defeat the rest of the Justice League in case they become villains and he continually has authoritarian tendencies for obtaining information and keeping tabs on people. He doesn't trust anyone but himself. That is central to the entire facade of Batman. His obsession with revenge leads him to put in almost every possible effort to stop crime, and that includes paranoia. The only rule that Batman has is that he does not kill.
That rule put into comparison with his psychosis, is the most interesting and important point of Batman. Although he is distant, cold, obsessed, paranoid, and at times cruel, he's still committed to justice. That's the strength of Batman. He has suffered the tragic deaths of his parents and the psychological impact of that and still maintains his ultimate sense of rationality and morality. This presents a compelling dichotomy: Batman is sane because he is insane.
As I've said, Batman is damaged, greatly so, but his moral code keeps him in check and helps keep his head about his shoulders, and that precarious balance presents a fundamental tension in his character that is not present in many other comic book heroes. All of the stories about the Riddler, the Joker, and even Kite-Man are just allegories for the mental state of Bruce Wayne. Batman isn't a comic book character that you read to watch him fight baddies, he's a character that you read about to see how his state of mind develops and whether or not he'll slip and lose what keeps him a hero. You read about him to see the eternal anguish he feels because of his parents' deaths. You read about him to see how he succeeds in his mission and how he fails.
What makes Batman compelling, in short, is that he is a psychologically damaged individual who ultimately maintains his sanity. His life is a balancing act, and that is the fundamental message and theme of every Batman comic you will read.