Marketing.
With the right kind of marketing department, you can make anything popular. Hence why a wealthy billionaire playboy captain of industry is able to to put on a mask, go round beating up criminals (generally of the working classes), apparently to defend the same laws that he so readily breaks himself... and this guy is a cultural icon?
It's all to do with catharsis, I think. People don't like to admit that ideas like crime, justice and the law are actually very complicated subjects. For the most part, it's too difficult for a lot of people to think that crime happens for various reasons, not all of them unavoidable, and that definitions of justice and law are based on the social notions of any given period, rather than being based on objective 'truth'. As far as a lot of people are concerned, criminals are scum who deserve to be punished, and Batman is a character who dishes out punishment by going round and beating the everloving shit out of them. Moreso than practically any other superhero, in fact. Most other superheroes are defined by their weird alien sub-plots, and crazy science-fiction overtones. Batman is the one notable superhero (honourable mention to The Punisher) whose raison d'etre is beating up criminals, not aliens or robots or interdimensional beings. People enjoy vicariously watching other people get punished for the wrongs they believe they've done, and Batman does that in the same way Dirty Harry does (if less lethally). No bureaucracy of law or due process, simply the justice of a righteously flung fist cracking into someone's ribs.
I personally find the concept of Batman pretty abhorrent. He's an ineffective hypocrite who refuses try and real effort to change Gotham for the better. He claims to want to uphold law and justice, yet his methods are illegal, and he works in direct opposition to Gotham's appointed police service. And he claims to want to stop crime in Gotham, yet he has never done anything to significantly reduce its crime rates. Ask anyone who's studied sociology, and they'll say that if you want to remove crime, you need to remove the causes of crime. The vast majority of muggings, robberies and burglaries are caused by poverty. People turn to crime when they feel they have no other option to get by.
We can see that Gotham has incredible wealth inequality. Does Bruce Wayne ever try and tackle this? Does he ever think that perhaps, by trying to reduce the wealth gap and bring more Gotham citizens out of poverty, he may remove the very incentive for which so many citizens become criminals in the first place? Fuck no. He's content to remain a billionaire captain of industry, profiting from the exploitative practises of his corporation, so long as it allows him to buy yet more expensive toys with which to beat up people on the street.
Batman's a psycho who uses his parents death as an excuse to act out on his own sociopathic tendencies. A large number of the villains he fights against became criminals directly because of his vigilantism (the Joker, Two-Face), while the low level mooks are working-class people forced to take desperate measures to get by simply because of how low Gotham has sunk them into poverty. He hasn't, to my knowledge, instigated any major campaigns to reduce the wealth gap, and just as importantly, he hasn't launched any campaign for prison reform, focusing on rehabilitating and educating prisoners to allow them to become functional members of society. A billionaire campaigning for social change and reform is someone I'd argue is trying to fight crime. A man who dresses as a bat and goes round punching people is a mentally unstable psycho.
What really galls me is the complete dishonesty with which the comics portray his actions. Perhaps Wayne has some philanthropic ventures on the go. I wouldn't know, as if he does, the comics give them only a cursory glance. Even worse, the man claims to have a 'no-kill' philosophy, yet the sheer brutality with which he beats up criminals means that he must, by this point, have killed someone.
Talk to anyone who works in an A&E ward, and they'll tell you how lethal even one wrong punch can be. People have died because their stomach collapsed from a wrongly thrown punch. People have died because someone broke their ribs, only to then have one or both of their lungs punctured. People have died from being punched in the face, and having complications from brain damage subsequently appear. People have died from being kicked in the back, and having their spinal column shattered. People have died simply from being punched, then breaking their neck on the pavement, or a wrongly placed table ledge, or a concrete stair.
Batman is a character who is supposed to be as strong as it is possible for a mortal man to be. The idea that he can go round beating up people as much as he likes, and because he doesn't use a gun or bullets they'll never die, is a dishonest one. In real life, Batman would have dozens of deaths on his hands now, people dying from complications from the injuries he inflicted on them.
When even famous comic writers like Alan Moore end up showing contempt for the sort of vigilantism that Batman indulges in, I can't bring myself to support the character. His entire appeal lies in a base form of vicarious thrill, the sort that comes from boiling down complex sociological problems into 'good' vs 'evil' binary dilemmas that can be easily fixed with enough punching. The fact that Rorscach is arguably the most deranged, violent and disturbed character in Watchmen is a damning indictment of everything that is wrong with the sort of vigilantism championed by Batman.
