The Lie:"It was out of character for Superman to kill Zod. Man Of Steel was, to put it lightly, a mess, made more disappointing because there was clearly an interesting deconstruction of a character we all knew hidden under the washed-out colour palette. It performed well, but not well enough to stop Warner Bros. going all in and enlisting Batman to save the sequel. One of the biggest complaints from audiences was the relentless, mind-numbing action, all of which culminated in Superman snapping General Zod's neck. A travesty, this was one of the worst changes to the mythology Zack Snyder and co. made."
The Truth: He's done it before. There were a lot of changes made to the mythology of Kal-El that felt forced just to give the story a 'new' feel, but killing Zod isn't one of them; it's Batman, not Superman who has that "no killing" rule. Go back to Superman II. The climax of the film has our hero de-power Zod and his followers before throwing the General down a cavern in the Fortress of Solitude. If that isn't murder then the eighties clearly had a different moral code.
Man Of Steel made a lot of mistakes in trying to update the character, but the killing of an almost unstoppable villain who's stated he'll destroy the Earth isn't one of them. The logic of doing it by snapping the neck of someone who thus far has been indestructible, however, is.