I think I finally understand what Mihawk said about Whitebeard, something about measuring the “distance” between them.
I think Mihawk’s isolation and absolute power make him almost clueless about his own strength. If you really think about it, he sort of lacks any real rival.
Gol D. Roger had Whitebeard and maybe Shiki. Garp had Sengoku and even Gol D. Roger.
The Yonko have each other and so do the Admirals.
But what about Mihawk? He lost the only real rival he had (Shanks) 12 years ago. TWELVE!
Whitebeard described their battles as legendary. It seems like Mihawk has spent those last 12 years alone almost (from a power point of view), which is funny because it fits his character. He sails alone, he lives in a castle alone, on an island by himself. This theme of isolation is Mihawk.
To add more, Mihawk in the series is treated as a sort of myth. Think back to Marineford when everyone was commenting on him. Pointing out his legendary (12 of its kind) sword, pointing out the menace in his eyes, and when it seemed like he was about to strike, almost everyone stood still, waiting to gauge whether the legend is true or not.
I like that word, gauge. The Admirals were gauging him, the Shichibukai were gauging him, almost in the same way that Mihawk was gauging Whitebeard.
The World’s Strongest Swordsman, alone in his power, testing to see where he stood next to the World’s Strongest Man. Above, below, equal? That’s what he was asking.
To add just a bit more. Mihawk typically doesn’t heed to the World Government’s call, but Marineford was the exception. It was the only permissible arena for Mihawk to fight any true elite. He can’t typically fight Yonko because that would be a declaration of war on them (and he could also be violating the World Government’s plans). He can’t fight Dragon… who knows where he is and that’s another declaration of war. He can’t fight the Admirals. And it’s fitting that Mihawk left as soon as Shanks arrived, almost signifying that their rivalry is over and that they’re just friends now.
Can you imagine being Mihawk? So powerful that you’re almost isolated in that power.
Zoro vs Mihawk will be legendary!
*Theory by barmanlagoon