Why Does Lex Luthor hate Superman?
There are many comic books that attempt to answer the question "Why does Lex Luthor hate Superman?" but I think 1960's Adventure comics #271 provides the most logical answer.
In Jerry Siegel's Adventure Comics #271, Lex Luthor saves Superboy from the debilitating effects of a kryptonian meteor and the pair quickly become friends. At this point in his life Luthor had been keeping his genius level intellect relatively secret but chooses to show Superboy his true potential.
In response, Superboy builds Lex his own research facility as a means of researching the "life-form" formula and a cure to kryptonite poisoning.
During one of Superboy's visits, a fire is accidentally started in Luthor's Lab. Superboy uses his sonic breath to extinguish the flames but the blast is far too strong. The fire engulfs the life-form, destroys the formula used to create it, and douses Luthor in chemicals which make him go bald.
The event causes a rift between the two characters because Luthor believes that his work was sabotaged out of jealousy. Luthor believes that Superboy destroyed the life-form because he knew what notoriety the discovery would bring and didn't want Luthor to surpass him in any way.
Siegel's book is the perfect setup to the historic rivalry between human and alien. I believe that the lab fire is what truly sparked (heh) Luthor's hatred for Superman.