Aoi considered herself a very... unshakable young woman. She didn't let others sway her opinions or ideals, remaining steadfast in her own ways no matter what life threw at her. Like a boulder, Aoi was proudly unmovable.
Until she met you. One of Urokodaki's little water style slayers.
Despite all the water style demon slayers she's met, you're the first one that's actually akin to it in her eyes. You change as quickly as the tide, can be strong or gentle, and seem to flow in and out of Aoi's life as you please. But it was the first time she saw you actually fight a demon that managed to move the once unmovable Aoi.
A demon had somehow managed to find the Butterfly Mansion, and both Lady Shinobu and Kanao were out on missions. Thankfully, you seemed to immediately emerge from the trees surrounding the mansion, effortlessly moving to take out the demon. Aoi felt as if she just watched something... life changing.
She had sworn off ever trying to be a slayer again, terrified of what could very possibly happen to her. Not even seeing Lady Shinobu's impressive feats have caught her attention as effortlessly as you did. So it was with great reluctance and a hint of embarrassment that she invited you in the Butterfly Mansion with the plan of asking you to train with her.