@lentinant Already mentioned one of the reasons why Nezuko is stronger than most other demons. It's because she was able to survive after taking a large amount of blood from Muzan Kibutsuji.
Muzan Kibutsuji may have tried to kill Nezuko by exploding her after injecting a lot of his blood into her veins. But she was somehow able to survive with that much of Muzan's blood, that's what possibly made her a powerful demon.
In one of the episodes, we see Muzan Kibutsuji frightened of Nezuko and Tanjiro's past relitave when he found the same earrings and scar on the face and ears of Tanjiro.
Apart from that, I would say her father was possibly a Demon Slayer too, maybe he was researching rare herbs or plants that could protect humans from becoming flesh eating Demons. He was maybe able to create a vaccine with which a human can control his/her will after becoming a demon too. He could have injected his family with the vaccine because he knew Muzan Kibutsuji would come after him & his family in future.
There may be some limitations on a vaccine, like how it should be injected before becoming a demon.