I love Batman and I'm not alone. Batman is more beloved by the internet than a Jesus made of bacon. The concept of Batman has changed a lot over the last 75 years, but its core quality is that it adapts to the culture of which it is a part.
Batman does have some problems though. While some of these are products of their time, many are the result of concepts executed without considering of the implications. I'm no Batmanologist, but I'd like to take a few days to look at these problems.
Early Batman was built in the mold of pulp heroes; an extraordinary man who has set out to fight crime with his extraordinary abilities. Compared to later superheroes, and even many of his contemporaries, Batman has no powers. He eschews most technologies, relying wholly on the physical and mental capacities of humanity, even decades later when he's matching wits with immortal aliens boasting entire war worlds. That's not the best approach; someone who wears circus tights and a tool belt is worthless in a world where villains can punch through metal, control minds, or have guns. After all, what can a guy do that even a second-rate hero like Hawkman--who is literally a guy plus wings--can't?
It is ridiculous, right? Eventually, shit would go down, or he'd just get unlucky and BAM no more Batman. That's even if the lifestyle of being Batman wouldn't just push a person to mental and physical exhaustion and the secret identity of the well-equipped, omnipresent crimefighter wasn't immediately apparent (spoilers: It's the rich guy whose parents were killed by CRIME.).
Even his mission is bizarrely defined. Fighting the idea of crime? If you've been paying attention, The United States has had a war on just one type of crime for the past thirty years or so and hasn't done a very good job of stopping the demand, supply, or distribution of drugs. One guy with an impressive budget using the same peace-through-superior-firepower approach can't be much more successful.
While studies which examine the social causes of crime are not incontrovertible, the answer to stopping crime is at least as many parts social and economic as it is brute force. Yet Batman uses unparalleled training and an array of cutting-edge, branded tools to arrest criminals so that others can inevitably take their place.
Until those very same criminals escape and resume business as usual. The universe of Batman features a Gotham criminal justice system which is both fascistic enough to convict criminals apprehended by a vigilante who does not give depositions and toothless enough to treat the insanity defense the same way a dungeon master treats grappling rules; claim it if you want, so long as they don't have learn how it actually works.
Certainly, if Gotham City's government were to prosecute and incarcerate these characters, as the public might expect of them, things would be different. If even a random cop would pull a gun on The Joker, you could claim Batman was working with a government that's trying to make its citizens safer. Within this environment, Batman's actions can not permanently reduce crime.
Then you get to the part where he starts recruiting kids. Ostensibly picks up Robin because he wants to help the kid cope with the loss of his parents. More modern interpretations where he intentionally targets Dick Grayson for recruitment as a form of extreme adolescent character-building, which should be disregarded as anything but well-illustrated parody, is still build on a troubling scaffold.
Batman opting to eschew, y'know, seeing a psychologist in favor of adoption and rigorous homeschooling to protect an orphan from the worthless, inferior external world—a series of actions indistinguishable from those of a very small cult—hints that Batman isn't concerned enough with Robin's welfare.
When you're on a lifelong mission to fight murderous, gun-toting gangsters by utilizing superior intellect, extensive ninja training, and punches, there's very little a post-pubescent, brightly colored, emotionally troubled sidekick really adds other than to reduce the average density of bullets in your vicinity (by incrementing theirs, of course).
That's even assuming Robin is recruited for something as well meaning, if flawed as fighting an impossible, never-ending war on crime: