Well, not hate to Mihawk, but seeing how a coward as Buggy is willing to be PK, might trigger something in Mihawk, as we all know he hasnt fought any strong fools.
He might realize that he is already the strongest but it is worth nothing if he forgot what it feels to have an extreme diff battle, the heat of battle, knowing you can die.
Maybe this will make Mihawk tremble in emotions he forgot and we will have the arise of the real WSS.
Maybe somehow, Buggy, Mihawk, Crocodile were silver medalist who lost their way somehow. We already saw Buggy giving up to reach One Piece since Shanks didnt want to. Crocodile lost his way after his defeat to Whitebeard. What if, Mihawk is equal or stronger than Shanks, but still lost to him? Why? Well, he had friends, allies, territories which is much more than what Mihawk did and might be able tk do for himself. Doffy right now also to, his dreams were taken away.
Buggy just put some fire to them, so they will arise once again.