Basically, Taylor Marvin, in his original post, says that Batman destabilizes Gotham to the point where the gov't does not have a monopoly on the use of force. That in return creates social disorder because human's construct societies on the basis that the state has a monopoly on the use of violence. We maintain order by telling ourselves that uses of violence outside of the state are illegitimate. And when problems arise the state can solve them through violence because we deem their action legitimate.
Erik Kain responded by pointing saying:
The central thesis, as I see it, is that Batman would be unnecessary if good people not wearing masks would actually stand up and recapture their own self-determination. A vigilante is not necessary for this at all. Batman is the option of last resort.
It should be said that this is the only way to understand Batman’s refusal to kill. For as much as he breaks the government’s monopoly on force, Bruce Wayne doesn’t want to supplant the institutions of Gotham, he wants to aid them. Killing a villain like the Joker solves the short-term problem of a murderous psychopath, but does immense damage to the long-term goal—by executing criminals, Batman flaunts the law in its entirety, and completely undermines the legitimacy of Gotham and its institutions.
I think this is correct. Batman wants to work with Gordon in order to restore the legitimacy of the state. And the state was illegitimate before Bruce Wayne decided to become Batman, as Kain points out. So Batman didn't create social disorder. It was already there. He was a reaction to it. But he did have an effect on the disorder that was already there. He helped make it worse by prompting a response from the Joker.
Then Jamelle discusses Bruce's motivation to become Batman:
Thomas Wayne was a philanthropist who sought to improve Gotham and the lives of its most vulnerable citizens. This, more than anything else, is why Bruce Wayne donned the mantle of Batman. It’s not that he’s “incapable of dealing with loss and forming real relationships,” it’s that he wants to build a Gotham where his childhood loss is never felt by anyone, ever again.
Put another way—as we see with Ducard in the first film—vengence will only take you so far. You need a positive goal to keep striving. Bruce wants a better Gotham, which is why he’s willing to endure the hatred of his home if that’s what it takes to build the city into something durable.
Again, I think he is correct. Check the link for why he comes to that conclusion. I wanted to add to this discussion by pointing out something Jamelle doesn't fully touch on, which is why Bruce didn't go strictly down the path towards vengeance. Remember that in Batman Begins Bruce is filled with anger when he comes back to Gotham in order to go to the hearing for the man who killed his parents, Joe Chills. In fact, he is attending the hearing so that he can kill Chills. But he doesn't get the chance. Falcone has someone kill Chills before Bruce can.
After Bruce sees the murder he talks to Rachel about it. He confesses to Rachel that he was going to exact justice himself if it weren't for Falcone's hit. But Rachel corrects him and says that vengeance isn't justice. And that is not what his father was fighting for. This is the turning point for Bruce. He realizes Rachel is right and that vengeance, or murder, is not the way to go. He confronts Falcone and realizes that he can't fight him and the social disorder that he has helped create on his own. And this prompts him to leave Gotham to find himself and figure out how to deal with the injustice in the city. He then becomes Batman.
But this all hinges on Falcone's hit man getting to Joe Chills before Bruce does. If Bruce gets there first he becomes the murderer and probably spends the rest of his life in prison. I guess we can debate whether or not Bruce would have actually gone through with it. But as far as I can remember, Nolan doesn't give us a reason not to think he would. After all, Bruce turns out to be the kind of person who dresses up like a bat and fights criminals. He is fairly comfortable with violence. And instead of going with Rachel and not watching Chills die like she wants, he makes a point to stand there and watch him die. In a way, he gets his vengeance. Just not in the exact manner he wanted.
And in the same manner Bruce becoming Batman depended on Falcone's hit getting their first, the existence of Batman hinges on Rachel convincing Bruce that justice means more than killing those who have wronged you, and that Bruce's father wouldn't approve of what Bruce was going to do. I'm not sure how this is directly relatable to the original discussion of social disorder. But it further clarifies how much the existence of Batman is tied to an already disordered society.