Because he's Superman. Where someone else couldn't find the way, he should have been able to. Like with the Elite.
He's supposed to be the symbol that makes the impossible , possible, and there should have been a clever way to stop Zod. Instead he snapped his neck infront of a family because the movie wanted to be edgy.
The characters aren't alive, they're fiction, so you can write them whatever way you want them to. Nobody force Snyder to have Superman in a situation where he has to snap a neck, just to make him darker. And for all the "you'll see how it affects him next movie" it didn't, it went nowhere, and it was shit.
I mean, I could write a story where Batman is force to snap Alfred's neck to save the Robins and Catwoman, and he probably would, but that doesn't mean it's a story worth telling or suited for the character.
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