For me. . . okay, I am not a huge fan of the traditional silver age Code vs Killing, at least outside of actual Silver Age comics or homages. I'm fine with heroes using deadly force, *when suitably justified*. I've never had a problem with pretty much any of the Marvel heroes, for example, and Wonder Woman has likewise been fine ( in morality, though one scene in the Snyder Cut is a little skeevy in portrayal ).
The problem in MoS vis a vis such is three-fold. One, the final battle itself was poorly framed for justifying use of deadly force. You could see what the director *wanted* to achieve, but it was just clunky. You want the only option to be to kill Zod, but then you do a fight where the only way he ought to be *able* to kill him is by having overpowered him enough as to make it unnecessary. Two, and much more important. . . I don't insist 100% that Superman never ever kill, but I do insist that he be greatly respectful of life. And that. . . just isn't really present in the movie in a consistent sense, at least after he puts on the costume. There is just way too much collateral damage that goes unnoticed by Superman, and that *should* bother him. For every scene with him rescuing someone, there's another scene of his battles blowing up entire buildings, without any cinematic acknowledgement other than "Hey, this looks cool!" Its not like Superman has to successfully save every single life, but he damn well should be portrayed as *wanting* to save every life.
Oh, three? The final scene with Zod hinges on the idea that Superman doesn't kill and doesn't want to kill, but they forgot to actually *put that in the movie*. Neither Jor-El nor Jonathan include that in their moral philosophy, and Clark never brings it up in his own angsting, so literally the only way to know why killing Zod is supposed to be such a traumatizing and life-changing experience for Clark is by bringing in outside knowledge from the comic source material. . . that the movie in general at best shows indifferent distancing. And no, I don't buy for a second "But everybody knows killing is traumatic!", not on a level where the trauma of taking another life is supposed to compare with the trauma of half of Metropolis being leveled around you.