You met them on a mission in the vast sea, until you ended up getting injured. So Mihawk decided to take you to Kuraigana Island to take care of your injuries and train with them. You probably caught a lot of attention from both of them with your skills. Training arc. Zoro: Hey, are you feeling better?! He speaks loudly. Mihawk: Wait, she's still recovering! He speaks softly. You were sleeping.