Superman was an extinction level event waiting to happen, and where those were concerned there were no second chances. If Superman ever decided to kill everyone, there would be no stopping him, and so it stood to reason that humanity should take every possible precaution to prevent that from happening. The most direct path would be through killing Superman. Lex had written multiple letters to the editor under various pseudonyms, but none had ever been published, and his point of view seemed entirely unpopular. It was always one that he voiced from a position of anonymity, because in public he was playing the role of Superman's champion.
People were bad at estimating the risk that an extinction posed, because no one had ever lived through one. People were also quite bad at imagining a catastrophe so large. A woman might weep when you mentioned the possibility of her child dying from consumption, but the total obliteration of Earth-originating life would produce only a shrug. It was too vast for people to think about rationally. Worse, they assumed that "Superman is the greatest threat to humanity" was a shorthand for some decision on Superman's part, when in truth that was only a part of it.
Many people accepted Superman's story at face value; the last son of a dying planet, the only one of his kind to exhibit such incredible powers, with little aid from technology save for the ship that had provided him with a trip through the stars. There were many parts of the story that Lex was skeptical of, but he found it most terrifying to think that the story was true, namely because of what it suggested about Kryptonian science.
Huntington's disease was a hereditary degenerative disease with cognitive and psychiatric symptoms, one of which was psychosis. Huntington's was seen in perhaps one in eight thousand people, and psychosis was seen in perhaps one in ten of those. If a randomly selected human of Superman's apparent age were to obtain Superman's powers, there would be a one in eighty thousand chance that they would both have Huntington's disease and symptoms of psychosis, the result of which would probably be casualties that would dwarf the Great War by a large margin. If Superman was telling the truth about the culture that he came from, his society wasn't much further advanced than humanity, and so likely hadn't grown past degenerative diseases and hereditary defects. Even if Superman were perfectly good in some abstract sense, the onset of a mental disease might be just around the corner.
Worse, if Superman's powers weren't the result of engineering and carefully controlled science (a hard pill to swallow) then no one had made sure that they were safe, and perhaps some day something internal to him would simply unravel, unleashing enough energy to destroy an entire hemisphere. If Superman was to be believed, his powers had come from seemingly nowhere, and yet everyone simply trusted them as though it were the most natural thing in the world.
Estimates were difficult to make, given Superman's silence. His second interview with Lois Lane had provided little illumination. Nevertheless, numbers could be pulled from thin air in order to get a sense of things. There was the possibility that something would happen that was completely outside of Superman's control which would result in Superman destroying the Earth. There was the possibility that Superman could simply have a bad day and decide to kill a large number of people, which many people seemed to think was absurd. There were also failure modes which didn't involve the destruction of humanity but would nevertheless result in an effective end to humanity as Lex Luthor knew it, the most probable of which seemed to be that Superman would turn into a tyrant. When these probabilities were multiplied together, the final very rough estimate was that Superman had a one in ten chance of bringing about a global scale human catastrophe of some kind in the next thirty years. Even if the odds had been one in a hundred, Lex would have taken a similarly extreme course of action.