Even the most far-fetched premise of science-fiction must attempt to get its audience to "suspend their disbelief" by coming up with plausible explanations that have some measure of a foothold in reality. That was a particularly tall order for Superman.
Originally, in 1938, Superman had great strength, resistance to conventional injury and could "leap tall buildings in a single bound" (about an eighth of a mile). Little by little, the comic books (Action and Superman) kept increasing his abilities, thanks primarily to writers of the radio show, newspaper comic strip and the Fleisher Studios' cartoon series.
In 1941, Superman #10 featured him actually defying gravity for the first time by hovering in the air, something the radio show had first introduced. Kryptonite, also introduced in the radio show, didn't make its appearance in the comic books until 1949.
But the outbreak of World War II put Superman's writers in a pickle that was widely discussed in the popular press. It was impossible for Superman not to get involved in the war, but it was a war he could certainly win within minutes - and that would be absurd and insulting compared to reality. Time magazine said of Superman in 1942, "As the mightiest, fightingest American, he ought to join up. But he just can't."
The Nazis noticed the irony, too. A 1940 SS newspaper mocked Superman: "Once there was a man so strong that he could stop a speeding locomotive with his ring finger, but he didn't do it."
For a while, Superman merely reflected America's isolationist position with storylines in which Superman forced the Germans, French and Russians to talk peace and dealt with Axis spies and saboteurs. But when all that disappeared after the US entered the war in 1941, writers began coming up with different excuses for his failure to intervene.
In the newspaper strip, Superman enlisted in the Army. But during his eye test, he became lost in patriotic thoughts and accidentally used his X-ray vision to read the wrong eye chart. Thus, he failed his physical.
In a 1943 comic book, Superman participated in war games with the US army - and lost. He concluded the military could beat the Axis without him.
Another dilemma discussed during the war was that Superman and Nazism were both directly inspired by Nietzsche's philosophy of "the superman" (or übermensch). Originally, Superman's powers were explained as due to his belonging to a genetically superior "super-race." In 1945, as the Nazi horrors became widely known, this explanation was changed to one involving the planet Krypton's red sun and stronger gravity rather than a super-race theory.