I have no issue with Superman killing if it serves the story and his character well, although I'd personally prefer that he always finds a way to avoid killing.

When Clark kills Zod and his goons in the comics he exiles himself into space due to his guilt and remorse. He also had decades of not killing in the comics to give the moment gravitas (yes I know it's a different Superman post-Crisis, but those decades still stand for the reader).

In the Snyderverse Clark kills without any build up. It means nothing. The very next scene he's smashing a satellite and a soldier is making a joke about how hot Clark is.

It's all in the execution and Man of Steel, and the follow up movies, handled it horribly.