In the fight against Zoro in the Baratie arc, Zoro revealed his three sword style to the world’s strongest swordsman, who broke a sweat after seeing it.
Zoro invented the three sword style, right? So Mihawk wouldn’t recognize it, right?
WRONG
In an SBS, it was revealed that Zoros father, Roronoa Arashi (which means storm), was also a swordsman killed by a pirate. Obviously, due to being descended from Wano, he had to be a pretty strong swordsman so a normal pirate probably wouldn’t be able to kill him. So maybe, after hearing about his strength, Mihawk went to fight Arashi, and won, but not so easily. Arashi used the Three Sword Style, just like Zoro, who “invented” the style because he only saw it once as a baby and couldn’t remember if it was real. When Mihawk saw Zoro use the Three Sword Style, he remembered Arashi, and broke a sweat. Anyways that’s my theory, but hey that’s just a theory— okay matpat you retired stop sneaking into my One Piece theory