@Rage Where on Earth do you live if killing can solve every problem? The MC's foremost problem is that Jilyu was already officially the hero who defeated the demon king. Jilyu had been made a nobleman already, along with an estate and everything, as a reward for defeating the demons. As far as everybody knew, Arga was just a retainer. Basically a nobody, even if a lucky nobody for serving under the mighty hero. Furthermore, Jilyu even managed to get witnesses to see how the MC supposedly went crazy and was going to draw his sword to attack the "hero". Everything's a lost cause at this point already. Kiling Jilyu would achieve nothing but make Arga known far and wide as a murderer who slew the hero.
Seeing Jilyu's incompetence and petty personality, it's entirely possible he won't rise high in his life anyway but will rather soil his own fame sooner or later.