It's like he never outgrew the teenage idea of what makes characters cool.
Yeah... He's stuck in the 1980s with
Watchmen and
Dark Knight and thinks that's all superheroes are. (Although he was around 20 when those came out.)
Although let's face it, to an extent, that's been true of DC in general for a lot of the past 40 years. But I think the comics have somewhat outgrown it by now, while Snyder hasn't.
I'm going to call you on this. There is a big difference between Batman in the comics and Batman in the movies regarding this question. In the comics, he may have killed in the early days of the 30s and 40s, but even then I think it was only in the earliest comics. In fact, he was as gentle as Superman for many years. By the time the fifties came around he was definitely not a killer.
Much earlier than that. The editors imposed the no-kill policy in 1940, about a year into Batman's existence, after an especially violent story where Batman strafed a truck containing one or two of Hugo Strange's monster men. Even in that story, though, Batman said on-panel that he hated to take life but had no choice.
As for Superman, he and Batman were equally lethal when they started out, since they were both emulating pulp magazine heroes, and they both got toned down in the very early '40s. In fact, contrary to modern expectations, Batman became a wholesome, police-sanctioned authority figure while Superman was still a vigilante hunted (but unofficially admired) by the police. Once Batman had Robin, he swiftly became a domesticated father figure while Superman was still a lone wolf. But before long, they were both equally legitimized authority figures using equally nonlethal and law-abiding methods.
The idea of them being opposite in their approaches didn't really emerge until the '70s when DC started making Batman stories darker and grittier as a counterreaction to the Adam West sitcom, and was codified by things like John Byrne's
Man of Steel reboot story where Superman and Batman were initially at odds until they realized they had common ground beneath their very different methods.
And in the movies he has always taken lives either by killing outright or by letting people die. That is the way he has been written after the Adam West version.
You wouldn't expect it, but even the Adam West feature film had Batman and Robin kill people, albeit unintentionally when the villains' dehydrated goons were accidentally rehydrated with heavy water and that somehow made them disintegrate when punched. (Though I think it was a little vague whether they were killed or teleported to an antimatter universe.) So technically they killed people, but it was an accident they regretted, and it was more the Penguin's fault for screwing up their rehydration.