I speculate, that in the world of One Piece, they held a tournament many years ago to determine the World's Strongest Swordsman. Mihawk participated in it and won it, & was granted the title. Now this is where things get dicey. I don't believe that that there was too large of a field of participants in it, Shiryuu didn't participate (in Impel Down), Shanks didn't participate (forming his own crew or still on Roger's Ship), Not many Wano people showed up.
Something similar to the Budokai's held in DBZ where Mihawk won one and never returned.
In summation, he hadn't tested his title, or wasn't challenged for it.
Something similar to the Budokai's held in DBZ where Mihawk won one and never returned.
In summation, he hadn't tested his title, or wasn't challenged for it.