Throughout the years, Superman has been sorely tested by some very bad humans and aliens but afaik, the number of times he had taken life has been very few and there has always been an extraordinary reason. His vow not to take life has been observed I would argue with much more faithfulness than any mortal human. Is it suggested that he is in fact constrained more by his vow than a human is even capable of being constrained?
A lot has been tossed about in this regard. Superman/Wonder Woman #3 kind of explored this in a modern context, where Diana Prince/Wonder Woman and Superman kinda have a thing going. And so, of course, who better to discuss this with than the socially well adjusted Batman
Superman's morality, for the most part, comes from a strong upbringing by the Kents. Their simple morals seeped into their adopted son and they turned him into a fine man. Who happens to be able to punch the moon into dust.
It's that last part that probably plays into the "don't kill" philosophy. Man of Steel (the movie) really delved into what happens when Superman isn't so concerned with saving innocent lives. Humans became collateral damage. While there are times you can't avoid that, Superman there doesn't seem to think that's priority #1 but maybe #2 or #3 (the order of rules is kinda important). Man of Steel wrecks a lot of stuff willy-nilly.
Modern Superman puts "Don't kill" at #1. Because, unlike Batman, if Superman gets it wrong you could be facing a holocaust really quick. Knowing you have a god-like being who has vowed not to harm you puts a lot of people at ease.