You could choose to see that as a low point for him in his war with the Mutants, as later on, he unequivocally rejects using guns. If you look closely at the picture, there is one spent casing, so one bullet fired. Since this was a public case with a kidnapping, if he had killed the mutant, this would have been in the news and later the talking head against Batman would have brought up the murder. The fact that he didn't kill her is made 100% clear (but not explicitly stated) within the book itself. I choose to look at it as lower numbered rules can be broken so long as higher numbered rules are not. ie. guns can be used, but only if they don't kill anyone.
I choose to see it as "Batman used a gun, ergo there is no rule that says Batman never uses guns."
It is a pretty big stretch from "Batman witnessed it", which is reasonable from his comment about "almost asking why", to Batman encouraged him. There's nothing to back that up. It's pretty clear that Batman's no killing rule is absolute, but cuts pretty close to the bone. If a scumbag responsible for arming gangs to kill people wants to take his own life, Batman isn't going to stop him (at this point in his career).
Yes, he used a gun, but this is one panel in the entire novel and later he explicitly rejects their use. Cherry picking instances like this is how Snyder and co. picked Superman killing Zod. It happened one time, so we can make it the new normal.
It is only cherry picking if I was trying to assert that Batman is comfortable killing people: see, he did it once, so it must be normal for him. I did no such thing. I asserted your rules about Batman have exceptions. I am only required to produce one to demonstrate that fact.
Just because I don't agree with you, doesn't mean I'm taking the exact opposite position of you. When I say that TDKR shows a Batman that has no rule against using guns, I'm not trying clumsily to say that Batman loves to use guns. I'm saying Batman in TDKR has no rule against using guns, at least no rule he isn't willing to break. If I meant more, I would have said more.
As I stated above, the Mutant didn't die or else Batman would have been crucified in the media. It is the death of the Joker (certainly more hated than any Mutant) that gives the authorities the official cover to want to bring him in. If a murder had happened earlier in the book, they would have gone after him earlier. So either there's a major public case where Batman murdered someone and the police, media and government covered it up and forgot about it, or the mutant didn't die.
Or maybe there were no credible witnesses to accuse Batman of murder. A lot of mutants die in Batman's wake when he first engages the mutant army, which is before the Joker's return, and even if you think Batman is responsible for none of them there's no way the media could know that (in the print version, the mutants shoot weapons at the bat-tank that very obviously result in inflicting casualties on themselves). If the media was as predictable as you claim they are in TDKR, they would have used that initial fight to hang Batman in public. It is possible that instead, the media knows it won't get a lot of public sympathy generated from the deaths of the mutants, especially in the case where they kidnapped a child or were massing an army. The Joker, however, was made a high profile case by the psychologist who was trying to make the case that the Batman was himself responsible for the actions of the Joker. That's something that can be spun in different ways.
In either case, if you are going to apply a standard of "Batman doesn't kill unless there is unambiguous evidence of the kill" then it is hypocritical not to apply that standard to BvS. When Batman hooks and drags the car around, there is no unambiguous evidence that Batman kills anyone. By *my* standard of evidence, I think it is fair to say it is highly likely that someone was killed in that sequence. But that same standard says it is equally likely that someone was killed in both the print and animated versions of TDKR. But by your standards, there's no proof Batman killed anyone in BvS. Everyone in it *could* have survived. Even the people he shoots in the scene near the end in his big fight: what's the mortality rate of someone being shot once by a handgun at close range? Pretty sure it is not 100%. Even the one guy that all reasonable people would agree must have died doesn't actually die on camera. There's no literal visual evidence of it.
Bottom line: Batman uses a gun in TDKR, which means TDKR does not obey a rule that Batman doesn't use a gun. Batman may not like to use guns, he may hate guns, he may encourage other people not to use guns, but he has no *absolute* rule about not using guns. And it takes a lot of effort to claim that Batman doesn't kill even once in TDKR, effort not being equally used to attempt to claim Batman avoided killing in BvS.
Incidentally, in this scene:
It is obvious that Batman isn't making a personal confession about his attitude towards guns. He is trying to make sure his army isn't a murdering mob. This is the next panel:
He's trying to keep some control over his followers, not making a New Years resolution.
