Between all of Tanjiro's skills and his mannerisms, Muzan is certainly scared of Tanjiro. Tanjiro represents and certainly ends up being the core threat to Muzan's quest to step back into the sunlight.
With his blood, Muzan can turn others into demons and seems like an unstoppable foe. However, the demon king seems to fear one thing: Tanjirou's hanafuda earrings.
Moreover, Tanjiro's appearance somewhat resembled Tsugikuni. So the only reason Muzan is afraid of Tanjiro is because of the Hanafuda earrings he possesses, which acted as a reminder of his downfall.
Hakuji threatened him but was silenced by Muzan piercing his hand through his head. The Demon King spoke of his plan to form a faction of twelve powerful demons and asked the young man if he was able to withstand the amount of blood he was given.
It is revealed that Muzan's true fear of dying and immense desire to live and survive was due to him being born "dead," where his heart would constantly stop in his mother's womb and was assumed stillborn until he fought to breathe before his cremation.
The only Demon he despises the most is the Upper Rank Two: Doma.
He sees himself as perfect since he is immortal and very powerful. The only thing he's weak to is the sun.
Who does Muzan regret killing? He shows his most human side to fans, wherein he admits to regretting murdering his doctor. He comments that had he been patient, the doctor would have cured him, and he would never have turned into a demon.
Anne was a kind and loving soul and was described as the only person that Muzan had truly loved, besides his three daughters.
Yoriichi Tsugikuni, the first swordsmen to ever use Breathing Styles, once nearly killed Muzan with Sun-Breathing, and Muzan has been both physically and psychologically scarred ever since.
Akaza is an upper-rank-three Demon and one of the most faithful minions of the Demon king Muzan Kibutsuji. The Blood Demon Art that Akaza uses is known as Destructive Death.
1) Kokushibo
Kokushibo stands at Upper Rank 1 in the Twelve Kibuki. He is the only demon to have a breathing style in the Demon Slayer series. In fact, Muzan views him as more of a business partner and one of his closest allies.
Sanemi Shinazugawa
In their initial encounter, Sanemi held a deep hatred towards Nezuko due to her nature as a demon.
Kokushibo is one of the strongest demons in the anime, only second to Demon King Muzan. Before turning into a demon, he was a part of the Demon Slayer Corps alongside his brother Yoriichi Tsugikini.
Muzan likely believed it possible that one day, Doma could become strong enough to survive sunlight, so killing him might've been detrimental to the reason Muzan made him a demon in the first place.
Muzan can detect the locations of his demons and can also read their thoughts. However, Nezuko and Tamayo are the only exceptions in the entirety of Demon Slayer, over whom Muzan has no control.
Curse of Kibutsuji
This curse besotted any who partake of Muzan's blood must be careful. The curse prevents Muzan's name from being spoken aloud, and any who do will meet a horrible demise. One demon, Susamaru, faced this reality when battling Tamayo.
Tanjiro Kamado
Tanjiro is considered to be Muzan's main nemesis throughout the series. After murdering the Kamado family, he was personally sought out by Tanjiro in Asakusa, Tokyo when the Demon Slayer recognized his scent from the scene of the murder.
Thus, Muzan created demons for hundreds of years even when he didn't want to turn someone. Since he didn't know anything about the Blue Spider Lily medicine, he needed others to find the plant for him by happenstance. This is the general reason why Muzan turned Nezuko into a demon.
He was plagued by health issues even in his mother's womb, and was stillborn as a result, but Muzan fought for life and began crying for the first time as his family was about to cremate his body.
In the first few arcs of the series, the identity of the demon that killed Tanjiro's family was a mystery. It is later revealed that it was none other than the series' main antagonist, Muzan Kibutsuji.
Muzan is someone who lives in constant fear of his own mortality. Despite being the most powerful being on earth, he's always afraid, he's always hiding himself, and he's always alone. He's a coward ultimately.
1 Yoriichi Tsugikuni (Demon Slayer)
Yoriichi's mastery of the Sun Breathing technique, combined with his incredible speed and agility, made him a formidable opponent for Muzan.
After he neutralizes Tamayo's poison and emerges from his flesh cocoon, Muzan's hair grows in length and turns white due to Shinobu's poison accelerating his age. He also grows numerous mouths all over his limbs, each one lined with a set of incredibly sharp fangs.
Demon Body: Unique from other demons, he possesses seven hearts, and five brains. These are responsible for his powerful vitality, should any of them be harmed, he will be severely weakened.