Oda blatantly explained Mihawk’s title. The strongest swordsman is the one with the best sword skill.
He is purely the strongest in terms of swordsmanship.
But just like the strongest boxer can still be shot to death if his opponent has a gun, being the strongest swordsman doesn’t inherently mean Mihawk can defeat characters who have significant skills beyond swordsmanship.
Sword skill is the ability to cut what you want and not cut what you don’t want.
Swordsmen who don’t use their swords to actually cut are still swordsmen, but they are less skilled than someone like Mihawk.
If Kaido replaced his club with a sword, he wouldn’t immediately become WSSM. To act like that’s all that matters literally devalues the art Mihawk and Zoro dedicate themselves to.
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He doesn’t fight Shanks because Shanks doesn’t actually care about swordsmanship.
He is a swordsman, but he uses his sword for haki beams and shockwaves.
It has nothing to do with Shanks’s strength. Mihawk literally faced Vista.
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The fact that Shanks has a higher bounty than Mihawk and is a yonko should give Mihawk ample incentive to take down Shanks, if they were truly rivals.
But they aren’t rivals. Shanks doesn’t care about swordsmanship. Mihawk dedicated his life to gaining the ability to cut anything. It’s what Zoro wants to be able to do.
Shanks literally doesn’t care about that and fights completely differently.