Why does Muzan despise Doma of the Twelve Kizuki in Demon Slayer?

Muzan Kibutsuji, who plays the Progenitor of Demons in Demon Slayer: Kimetsu no Yaiba, has little respect for his creations in general. Among the Kizuki, he has a few favorites, including Rui (Lower Five), Gyutaro (Upper Six), and Akaza (Upper Three). Koyoharu Gotouge, the manga's writer, revealed Muzan doesn't particularly like Upper Rank Two demon, Doma, in an official Demon Slayer "fanbook," though. Muzan is not opposed to killing demons he doesn't like, even if they are Kizuki, as Lower Ranks Six, Four, Three, and Two can confirm. So how did a demon that Muzan doesn't like rise to Upper Rank Two? Why doesn't Kibutsuji simply murder him, then?

Even though Doma is by far the friendliest and most courteous of all demons, he is known as the bane of Akaza's existence since he causes trouble everywhere he goes. Since Akaza was a founder member of the Kizuki, Doma joined much later but swiftly overtook Akaza in terms of power and standing, which is why Akaza hates Upper Two. Doma offered to meet up with Nakime for a love encounter, but Nakime politely declined since Kokushibo, Upper Rank One, treated Doma like a subordinate who needed to be lectured. Muzan might simply find Doma to be as unpleasant as everyone else.

Doma Has Surprisingly Poor Skills

When Muzan called the Upper Ranks together in the wake of Gyutaro's death, he angrily questioned why none of them had eliminated the Demon Slayer Corps or located the Blue Spider Lily. While Doma offered to gouge his own eye out in repentance for having recruited Gyutaro, he also admitted that he never found the Blue Spider Lily or Ubuyashiki because he's no good at detective work. Surprisingly incompetent for the third most powerful demon in the world (behind only Muzan and Kokushibo), Doma couldn't even get through the first gathering of the Upper Ranks in 113 years without annoying Akaza into punching off parts of his head -- twice.

Muzan Kibutsuji certainly seems like the kind of man who would kill someone for the high crime of Being Really Annoying. Yet strangely, Doma is left free to do as he pleases -- running his house of worship called the Eternal Paradise Faith where he eats his followers so they may live forever as part of him. Doma's penchant for eating women may play a big part in why he became so powerful so quickly, as he once commented that women are extra nutritious for demons thanks to their ability to nurture babies with their bodies. Doma's power as Upper Rank Two of the Twelve Kizuki is most likely what keeps him safe from Muzan's penchant for murder.

Doma had potential, therefore Muzan refrained from killing him

Muzan admitted that he had never intended to create further demons at the end of the "Swordsmith Village" segment of the manga. He only did it because he believed one of the demons might grow strong enough to endure sunlight. Muzan would acquire the strength for himself and realize his goal of becoming the ideal being if he were to swallow such a demon. The most likely explanation for why Muzan never killed Doma is that he couldn't take the chance of losing such a strong demon. Doma may have been made a demon because Muzan believed it was feasible that one day he may grow powerful enough to withstand sunlight; therefore, murdering him might have undermined that belief.

When Muzan slaughtered most of the Lower Ranks, he likely did so confident that none of them could ever be powerful enough to withstand sunlight. Doma, on the other hand, had too much potential to justify killing him just to get him to stop talking. Once Nezuko Kamado became immune to sunlight, Doma was surely kept around for the inevitable conflict with the Demon Slayer Corps, in which Doma succeeded where even Akaza failed by killing one of the Hashira, Shinobu Kocho. At the end of the day, Doma's potential outweighed his annoying personality, even if only barely.