Webthey have no reason to trust a demon with a special sword, especially when the materials are rare and special.
Fourth, nezuko is perfectly fine at fighting demons without one.
Webnezuko punched the swamp demon hard enough to cause him to cough blood and was capable of overwhelming the demon with powerful punches and kicks.
As she has no.
Webnezuko points out that the demon is still chasing humans despite being headless, putting tanjiro in a difficult spot.
Nezuko ultimately makes the decision for.