Except Bruce has seen things that has affected him at a personal and fundamental level. If any one of us were in his position, I really doubt that we'll be able to have the inner strength to continue the no-kill ideology. Eventually, the "filth" gets the better of you. After all, Batman is still human despite his glorious features. Think of something like police officers or military men, they have seen some **** in their lives and some of them react very harshly as a result of the experience, while others may withdraw from society, and some may be caught in limbo, not knowing what to do with their lives after having gone through that traumatic experience. Another point of similarity is how the events of Bruce and Jim lying about Harvey, as well as Rachel's death in TDK resulting in Bruce becoming reclusive. People thought he shouldn't have retired but it made a lot of narrative sense and brought home the point about the man behind the mask being human.
In fact, it's not that easy to say "Batman should know better" and it's treating a grey area as if it should be black/white. For all we know, Snyder's Batman in his origin might have had a no-kill rule that degraded over time. Primarily because he witnessed how much more cruel criminals are, and that his way wasn't going to stop them from doing what they are doing. In the face of cruelty, maybe Batman feels that the only way he can save Gotham is by being cruel(er).
From a writer's POV, it would be an interesting way to communicate how Idealism can transform into Machiavellian ideology.