Mihawk losing to a YC is as stupid as thinking Zoro is getting his katanas destroyed.
A lot of people keep talking a lot of nonsense about the current strongest man in the world, some say he will ask Shanks to help him from marines, a stupid theory Shanks fans come up with because they hate the fact Oda will have Shanks lose to Zoro so they think if Mihawk is there then it wont happen.
Some kept saying Mihawk will lose to Shiryu because they didn't want Mihawk to be stronger than a yonko so they wanted him to lose to a mere YC, some even to this point think Mihawk is weaker or equal to a YC 2/3 in Vista, forgetting the fact Zoro is fighting and beating a YC1 who is proving to be the strongest YC1 and yet implications are that Zoro is still far off from his peak.