system
Given the following post, respond as if you're commenting on Reddit:
human
Why is Lex Luthor Superman's arch-enemy?

Regular old guy vs alien from another planet.  What keeps Superman from just throwing this guy in jail?  Why Lex and not someone like Doomsday or Brainiac?  Granted, I'm not a huge superman fan, but this relationship always seemed really interesting to me.
gpt
Well, Lex really isn't a "regular ol' guy", he's literally the smartest human being on the planet (and several others). A charismatic and strong leader on one had, and an egotistical, obsessive and petty man on the other. 

For the most part, Luthor is jealous of Superman and his power. He often speaks of his fear that one day, the world will worship Superman like a god as he fixes everyone's problems forever. Humanity will stagnate and become useless under the heel of the Kryptonian. Lex hates useless things above all else. While he doesn't hate the idea of the world worshipping HIM, he would at least lead the world as a human being and not an alien.  

Besides, it's very likely threats like Doomsday or Brainiac wouldn't have arrived if it weren't for him. (Well, maybe not, but like Batman, you can argue the hero/villain arms race also happens with Superman) And sometimes, Doomsday can be controlled. Braniac can be bargained with if you know how to deal with him, and Lex is intelligent enough to know exactly what to say.  

Overall, Luthor is the mental match to Superman's physical powers, and he just can't stand the idea of someone out there he can't buy, bargain, kill or destroy. 

As for why Superman doesn't just throw him in jail, most of the time Luthor's hands are kept legally clean of any nefarious schemes he comes up with. He's rich enough to hire the best lawyers in the world, remember. He can also just instantly pay any bail set by a judge, no matter the cost. And then he'll buy the courthouse and jail to boot.