I just did a Google search on how many times has superman killed. In the main continuity it was the three villains in an alternate reality. Other than than there really are no other true killings listed. He blew up a star eater and sent some villains somewhere they might have died but other than exposing kryptonite to an alternate Zod that's about it. So I don't know where this belief comes from that he kills all the time.
In Superman #1 we see Superman throw a man who was questioning some soldiers off a cliff and destroy an enemy plane.
Here Superman blows up a munitions factory in broad daylight, there had to be dozens of workers in there if not more. Next we see Clark Kent put three criminals on trial and he even takes the stand against them in Court to secure the death sentence for all three of them. Superman is apparently pro death penalty and he does it all to impress Lois Lane, not from any burning desire to see justice done.
Superman allowing a domestic terrorist to die by his own toxic creation while he begs for help and Superman stands by and actually torments the would be terrorist as he is choking to death.
Superman catching a bomb dropped by an aircraft, that's certainly heroic enough. Until he throws the bomb back at the aircraft, destroying it. And in the next panel we see Superman sabotage a criminals brake system while they're driving down a mountain. Superman then escapes with Lois while the two occupants plummet to their deaths.
Superman #6 when two cars fall off a mountain, one works for The Daily Planet and the other is a car full of criminals. It's an easy guess who Superman saves but he is not the least bit conflicted by the criminals deaths, Superman even says "A well deserved fate!" while scanning the fiery wreckage. The next panel is an especially interesting one.
A cunning citizen discovers Superman's identity and tries to blackmail Superman. What was Superman's response you might be wondering, "Hasn't it occurred to you that
I could snap your neck with these fingers and I'd never have to worry about being exposed!". Needless to say, the citizen is terrified and he runs for his life with Clark Kent in pursuit. The citizen gets to a flight of stairs and declares that he knows Superman's identity but Clark Kent manages to get in front of the man and then the man mysteriously tumbles down the stairs and dies before he can spill Clark Kent's secret. Whether Clark Kent pushed him down the stairs or not is not clear so it's up to you to decide but it is an extremely convenient accident.
a would be assassins bullet ricochets off a wall and kills himself and the ever altruistic Superman quips "A murderer's fate!". When Superman rushes to a building it is blown up by a demolition crew yet for some inexplicable reason, Superman catches some falling steel and throws it directly on top of some innocent bystanders. The caption says that Superman threw the debris in an empty lot but you can clearly see it squashes two civilians. The civilians are even screaming "NO, NO!".
Superman #8. We see Superman scout out a hidden army consisting of at least two platoons, so Superman takes it upon himself to kill every living person he found there. Superman even says that there's "
Not a soul left alive - except for myself!".
Action Comics #585 and most people who argue that Superman never kills, regularly quote a frame from these pages entirely out of context to support their own argument of Superman's stubborn refusal to kill. "Nobody has the right to kill. Not Mxzyptlk, not you, not Superman... especially not Superman!". But what they never disclose is that Superman had literally just murdered Mxzyptlk on the previous page, Superman actually said to him,
"That's right Mxzyptlk, time to die!".
In Superman #82 Superman killed or destroyed Hank Henshaw and although Hank Henshaw was a sentient cyborg, he still had a consciousness, he still possessed Hank Henshaw's mind and thoughts. This is an often used and abused, creative 'out' for Superman, to have him fight robots but even this is inconsistent. Superman has trashed and destroyed countless cyborgs and sentient robots over the years yet we know for a fact that Superman values artificial intelligence as a legitimate form of life. Superman has even held funerals for Red Tornado and Tomorrow Woman.
Action Comics #805. Superman breaks Zod's neck again although apparently not quite enough to kill him but Zod charges straight back into battle and Superman viciously elbows Zod in his stomach and Zod literally drops dea
Superman #03, In an attempt to free a hostage from an alien sentience, Superman unleashes the full power of his heat vision upon her alien form expecting to kill her, Superman even begs for forgiveness as he does it and while he ultimately doesn't kill her, Superman did fully intend to end her life for the greater good.
Here Superman is mercilessly dealing with Darkseid's force of parademons who are undoubtedly 'living' and 'breathing' creatures in Justice League #3