As the demon cried into your shoulder and sobbed he said

“I tried I really did…!” Aizetsu said through tears as he bawled his eyes out.

Aizetsu had failed to kill a demon slayer and let them run away and his brothers were now mad at him. Aizetsu was the Upper moon four’s manifestation of sorrow. It wasn’t uncommon for him to cry. At the moment your his only friend and you are also a demon.