Mihawk holds great pride in the art of swordsmanship and honors the swordsman codex. Why did he consider air bar user Shanks out of all people his rival? Not only is Mihawk's interest limited to swordsmen he considers peers, having Shanks as his rival implies that Mihawk himself considers Shanks the greatest swordsman he could face, outside future Zoro.
Or is it, that Shanks, who was called top class swordsman in the Databook, has a "beloved blade" with a "long history of battles", that is most likely a supreme grade blade and was considered rival by the greatest swordsman himself, chose to throw away the skill he honed for decades in exchange for air bars that aren't considered swordsmanship? Or is it, that air bars performed skillfully with the blade, are part of swordsmanship?
Or is it, that Shanks, who was called top class swordsman in the Databook, has a "beloved blade" with a "long history of battles", that is most likely a supreme grade blade and was considered rival by the greatest swordsman himself, chose to throw away the skill he honed for decades in exchange for air bars that aren't considered swordsmanship? Or is it, that air bars performed skillfully with the blade, are part of swordsmanship?