Muzan is a very cold individual, the lower moons consistently disappointed him, and Enmu showed no fear while Muzan killed the other lower moons, which impressed him.
The wiki does a very good job of explaining Muzan's personality, and how he feels about humans, and his subordinates:
Muzan is cold-hearted, ruthless, intimidating, and exceptionally intelligent. He sees no value in any humans he has encountered and shows little value in his own subordinates. Rarely ever visually upset or happy, he appears completely monotone and detached on most occasions, even when he callously murders his own subordinates.
He tends to be very short-tempered too; he once killed two men and their female companion for simply being rude:
He brutally killed a pair of drunk men simply for being rude to him, and killed their female companion when she had done nothing, all while proclaiming his own perfection and superiority over them, displaying his pettiness as he won't settle for any mockery and will do anything he pleases until the humiliation is remedied.
Killing the lower moons helps to solidify just how cold and heartless Muzan is. When he killed the lower moons, he did so because he had become frustrated by their constant failures, as he began killing them, two, three, four, and six all showed great weakness in the eyes of Muzan by begging for blood, fleeing, denying his opinion, and attempting to flatter him:
After the demise of Kyogai and later Rui, the Lower Rank Five, Muzan was frustrated by the Lower Ranks constant failures. He called the Lower Rank One, Two, Three, Four and the current Six to a meeting, rebuking them and believing he no longer needed the Lower Ranks. As a result, Muzan started to kill the Two, Three, Four and Six one by one, as they respectively were begging for Muzan's blood, trying to flee, trying to deny Muzan's opinion and trying to think about flattering his master.
During this entire event, Enmu showed no fear and demonstrated a more sadistic demeanor which impressed Muzan, subsequently saving his life:
Enmu, the Lower Rank One, was the only Lower Rank left. However, unlike others, Enmu showed no fear over the brink of death and even nonchalantly accepting it for pure excitement. Enmu's sadistic streak impressed Muzan, and he sent Enmu on a mission.
Feel free to do some further reading on the official wiki, and on the villains wiki, which are the sources that support my answer.