Batman is evil. He isn't a rogue, he isn't a vigilante, he isn't a loose cannon. Far, far from it. He is Lawful Evil.
How many people have expressed contempt that superheroes with staggering mental, technological or supernatural powers waste their time "fighting crime" instead of helping humanity?
That isn't a coincidence. They fight crime because it's inoffensive. They fight crime because it's what the herd wants them to do. They fight crime because it's Lawful.
In other words, all those "superheroes" in comics are of Lawful alignment. But strict obedience to higher authority says NOTHING about whether a person is good or evil.
Once the two dimensions of character alignment are sharply and violently separated, it's possible to arrive at certain conclusions which would appear strange at first sight.
The typical scientist or bureaucrat is Lawful Neutral. The typical two-legged cattle is True Neutral. The typical protestor is Chaotic Neutral, caring absolutely nothing for good or evil. So far nothing terribly surprising, just insulting.
Then we have Hal Jordan in Emerald Twilight who tried to eradicate the Green Lantern Corps. Why?
Well, before his motivations were retconned, he had come to the realization that there WASN'T any justice in the universe and that the Corps may have stood for Order (Lawful) but it didn't stand for Justice (Good) therefore it had to be removed.
Hal Jordan was a Neutral Good character who joined up with a Lawful organization when it seemed Good and ruthlessly crushed them when he determined they had lied to him and that they were not so good. That they were despicably Lawful Neutral.
It's important to note that Hal Jordan's motivation was to resurrect his city because an evil had been done to IT. Not because an evil had been done to HIM. And that's the key fact we need to be able to judge Batman.
Batman is evil because his only motivation is HIMSELF. He fights crime because Gotham is a Chaotic Neutral City and because the criminals he fights are Chaotic Evil. Gotham's criminals are as antithetical to Batman as Neutral Evil is to Neutral Good.
The important point is that Batman's crime-fighting adventures have fuck-all to do with whether he is Good or Evil. Because they ONLY have any weight on whether Batman is Lawful (he is) or Chaotic (he hates that).
Now, Batman COULD HAVE BEEN Lawful Good or Lawful Neutral, but he isn't. He's a billionaire and you don't see him doing any good with his money. You see him being a playboy and selfish.
Batman's motivation for crime fighting was that his parents were murdered. Because an evil thing was done TO HIM. Not to others, but to himself. Selfish selfish!
And Christopher Nolan knows that Batman is evil because in the movie Batman Begins, Batman saves his sweetheart at the cost of millions in property damage.
Now, if Batman is the ultimate Lawful character, if his biggest motivation is Law, then how could he possibly commit millions of dollars of property damage for PERSONAL GAIN? Only if personal gain was as big a motivation could that make sense. But what that means is oh yeah, Batman Is Evil!!
And the only superhero to have ever been Neutral Good was swiftly balderized and his actions reinterpreted as a "fall".