Nezuko is able to cling to all the humanity she has left and she can also block his influence on her. Her strong desire of protecting her brother and the devotion towards her family makes her hard to control for Muzan.
Moreover, while she was asleep, Urokodaki performed a unique hypnotism on Nezuko, making her believe that all humans are her family and she must not hurt them in any way. With her immense fondness for humanity, Nezuko broke out of Muzan's control, becoming free to do anything at her will.
Nezuko, on the other hand, never was under Muzan's curse, it would seem. Instead, she used her will to protect her brother and other humans to fight off the curse. This is probably why Nezuko sleeps instead of eating humans. This also means her strength as a demon is based on her will to protect rather than feed.
Fans later questioned the reason for letting Nezuko live. Fans believed this could have been a strategic move from Muzan. The theory states that Muzan wanted to create a demon that developed an immunity to the sun. Upon doing so, he would consume the aforementioned demon and become invincible.
Her most prominent trait is her extraordinary growth rate, possibly due to the high amount of blood she received from Muzan Kibutsuji when he turned Nezuko into a demon and the fact that she doesn't need to consume human blood to survive.
So, in conclusion, her coming from a Sun Breathing user's lineage and not relying on human substance are perhaps the reasons for her immunity. Hence, Muzan was searching for the Blue Spider Lilly, a flower that was a crucial ingredient in the medicine used by the doctor who saved his life.
Secondly, Muzan would probably… eat Nezuko and Tanjiro in the hopes of obtaining their sun-resistance abilities, and also since he wouldn't be able to convince them to become demons to work under him. This would allow him to become the ultimate demon.
Akaza was also one of Muzan's favorite demons out of all his subordinates. The reason behind this is Akaza's extreme loyalty to his master. The Upper Rank Three demon was always sent away on special missions, something the Upper Rank 1 and 2 were often denied of.
In episode 6 of Demon Slayer season 2, Nezuko entered a berserk state to protect her brother Tanjiro, causing her body to develop into that of an adult. She loses her gag, grows a single horn and gains vine-like patterns across her body.
During his final struggle, and as a way to slow down the effects of the sunlight, Muzan adopts an enlarged demonic infant form, approximately as tall as a 3 story building when standing up. In this form he has very pronounced blood vessels across his body, small claws in his hands and fanged teeth in his mouth.
Nezuko, Tamayo, Yushiro, and later Chachamaru are the only four demons not under the control of Muzan.
Muzan Kibutsuji (鬼舞辻無慘, Kibutsuji Muzan) is the main antagonist of the Demon Slayer: Kimetsu no Yaiba fantasy action manga and anime series. Muzan is the powerful King of all the Demons, who has the ability to inject his victims with blood that allows him to convert them into more Demons.
And the Wind Hashira, Sanemi Shinazugawa, draws his sword against Nezuko…
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. More specifically though, was the fact that Nezuko was of Kamado blood.
Muzan, the King of Demons, is the strongest and also the primal demon in the world of Demon Slayer. Consuming his blood is enough to turn you into a powerful demon. He can control all the demons in existence, with only people with strong willpower like Nezuko being an exception.
Apart from that, Muzan doesn't hate Akaza because of his obedience. The only Demon he despises the most is the Upper Rank Two: Doma.
While she might not be as powerful as Muzan himself, her overall strength makes her easily comparable to an Upper rank demon.
Nezuko doesn't stand a chance against the Upper Moon 3
Nezuko is undoubtedly a strong demon in Demon Slayer and she proved her strength repeatedly. One situation that really displayed her true potential was the fight against Daki. She underwent a transformation and thoroughly overwhelmed the Upper Moon 6 demon.
However, the trait that sets her apart from all other demons is the fact that she has the ability to conquer the sun, prompting the Demon King to call her the "chosen demon". Abnormal Demon Physiology: As the "chosen demon", Nezuko has several unique demonic traits that set her apart from all other demons.
Haruka Shiraishi: Muzan's Daughter.
Tsukito, Yorogi, Kuraku, and Isatsu all agree that they are loyal to Muzan.
Her final human transformation occurs in Chapter 196 of the manga. Ultimately, Nezuko survives and finally turns into a human after being stuck as a demon for so long. Despite turning into a human, she's one of the prime reasons why Tanjiro could defeat Muzan, even after almost being turned into a demon himself.
Most of them had lethal wounds and died shorty after the battle; if they didn't die, they had wounds that would impede their fighting. If Muzan escaped, he'd stop fighting, save his energy and Tamayo's poison would eventually stop working, meaning he would come back to his full strength once again.
As it turned out, the scar on Tanjiro's forehead did have some significance to it, rather than simply being a Todoroki-esque burn from scalding water. Tanjiro wasn't born with this scar on his forehead. Rather, he acquired it when tackling his younger brother out of the way of a falling pot of boiling tea.