Nezuko is just a normal half demon, right?

NOPE!

One day, you, Tanjiro and Nezuko were on a mission in a village, a demon has been kidnapping children at night. You went with them because you’re a Hashira.

However, during that battle, Tanjiro got hurt bad and that pissed Nezuko off, she threw her bamboo muzzle off of her mouth and went full demon mode, with you helping her weaken the demon of course.