Superman is not a killer, however capable he is of the deed, it's never his intention.
In general Zod's case, he knew no other way to stop him but to kill him once he had him in the position to break his neck.
Superman's evolution on earth had rendered him more powerful than Zod, but not as skilled of a fighter.
After seeing no end to the constant bludgeoning between them, it left him with no other choice...and this is why he cried out after doing so.
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Zod does say at one point - "I was born a warrior.
I have had a life of training and adapting" and he proceeds to hover.
But the point is that, he was still learning to function in Earth's environment whereas Kal has 33 years to do the same thing.
I think it is very safe to say Kal was more powerful than Zod.
You may ask, how come the last fight took so long then?
Again, this is the first time Kal is engaging in battle whereas Zod has probably been in numerous battles.
So it was a good match but in the end, adaptability won.
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Superman was more powerful than Zod.
In one scene Zor-El says to Zod that his son was twice the man he is.
He also states that due to living on Earth, adapting to Earth's environment, his son has become more powerful.
So Superman had the strength which other Kryptonians didn't have and that is why he could break Zod's neck.
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It's just the case of adaptability to earths environment and also evolution.
It made Superman powerful as his skin soaks in the sun's radiation unlike Zod's.
Also, a human can break a fellow human's neck but
not a dinosaur's, similarly a Kryptonian breaks another Kryptonian.
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According to the film's official novelisation , Superman was able to break Zod's neck simply because while Kryptonians are far stronger than humans (making it impossible for a human to have snapped Zod's neck), Kryptonians are perfectly capable of inflicting harm on each other .
Note that what look like mere punches and kicks in the earlier fight sequence would have resulted in a human dying instantly .
They fought savagely, hand-to-hand, upon the floor of the station.
Their superhuman blows inflicted damage no human weapon could match.
Indestructible Kryptonian fabric ripped in the struggle.
Vicious kicks and jabs, delivered with Herculean force, left their faces bruised and bloodied.
A fist of steel split Zod’s lip, and he retaliated by driving his knee up into Superman’s chin.
The blow, which would have sent a cast-iron safe into orbit, loosened Superman’s teeth.
He tasted blood.
But Zod’s unreasoning rage made him sloppy.
He charged like an animal, lowering his guard long enough for the Man of Steel to deliver an old-fashioned haymaker that sent him flying backward across the terminal.
Zod hit the floor hard, only to discover that Superman had already shot across at super-speed to be there waiting for him.
And then the coup de grâce, against a severely beaten enemy...
A little girl sobbed as the beam came closer, now only moments away.
Superman cried out in anguish, knowing he had no other choice.
It was Zod’s life—or the lives of innocents.
He marshaled every ounce of strength that remained within him.
And then... He snapped Zod’s neck.
His form went limp, his fiery gaze extinguished instantly.
Superman released the body and let it slump to the floor.
Gazing down at the dead Kryptonian, he was surprised by the peaceful expression on his face.
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Superman doesn't kill anyone.
DC Comics and Christopher Nolan were not convinced with what Goyer and Snyder had come up with but later they approved of that move.
Superman is powerful on Earth than Zod but in many ways Zod is stronger than him.
Superman did not want to kill him because he just wanted to stop him from doing what he wanted to and both of them wanted Krypton to be build
but Zod wanted to do it on Earth, killing all humans which Kal-El disapproved of.
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Kryptonians on earth are immensely powerful, not invincible, not immortal.
Kal-El was able to snap Zod's neck because he alone had the power to do so.
As to why Zod could not do it-
It requires great skill and power to twist someone's neck.
This cannot be done easily and requires some sort of a lock on the opponent.
Kal-El never had any fight experience, while Zod was a veteran.
Though their powers were on a similar level, Kal-El would always be more powerful due to the long exposure of sun on his body.
Zod was barely granted powers and he could take on Superman.
While Kal-El always refrained from his powers at a mental level.
The scene where Zod tries to kill those people with his eye-lasers, sent Kal-El into a mental desperation to stop him.
Not wanting to be a repeat of the situation where Uncle Kent died, Kal-El used all he had to try and stop Zod.
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I think them being indoors could be significant, in direct sunlight they seem evenly matched but out of the sun Superman would retain his powers whereas Zod would diminish slightly and become vulnerable.
This is what I'm hoping, otherwise he should've snapped all their necks before they made a real mess of Earth!
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At the end of  Man of Steel , Superman breaks the neck of General Zod. My question is, how could he do that so easily? And why did none of the Kryptonians think about doing that to him? Especially, considering that they are a lot more ruthless and don't pay attention to morality, etc.  To be honest, I was a little confused when Superman broke Zod's neck because I thought it is not possible.
How did the final confrontation in Man of Steel get resolved?
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<plot-explanation><man-of-steel><dc-extended-universe>
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Uper man doesn't really want to kill him, also because they both wanted to build Krypton. But, Zod wanted to build Krypton on earth, killing all humans which Kal-El disapproved of.  DC Comics and Christopher Nolan were not convinced with what Goyer and Snyder had come up with.
Superman doesn't kill anyone. DC Comics and Christopher Nolan were not convinced with what Goyer and Snyder had come up with. Superman is more  powerful on Earth than Zod but in many ways Zod is stronger than him.