And don't forget in HUSH he was going to kill the Joker and Gordon stopped him.
These heroes are not perfect. I just saw Wonder Woman this weekend because I got the Blu-ray and I see even she killed the wrong guy. Dude wasn't even Ares. SHE was convinced it was Ares and Steve tried to tell her, "maybe he's not Ares" but she went ahead with what she thought.
Same with Bruce. The worse thing Bruce feels he can do is cross that line and kill a rogue or innocent, whatever. Now Selina knows for herself from his lips that is his line and that is his ultimate heartbreak. She knows his deepest fear from his mouth.
All of these heroes have fears.