Even before 1010 I already thought that Mihawk didn't had Conqueror since he didn't taught Zoro. I was already sure Zoro had it even without a statement.
Now to me is more than clearly that Mihawk doesn't have that is why he never realized Zoro had it.
They trained for 2 years Zoro for sure showed Ashura. This is head cannon assuming Ashura is the Conqueror. But Zoro has others fears similar to conqueror as his fight with Monet. Pretty sure someone like Mihawk with conqueror would realize that and teach him about it.
Mihawk wants to someone to surpass him. Initially would be Shanks. Maybe Shanks just keep up with Mihawk because of that. But Mihawk honor wouldn't accept to fight and lose to an one armed man. Mihawk then see in Zoro the same qualities Shanks has and expect to be surpassed by him. Oden and probably Ryuuma had greater potential by having Conqueror that Mihawk will never reach so he himself knows he can't be the strongest forever.
Now to me is more than clearly that Mihawk doesn't have that is why he never realized Zoro had it.
They trained for 2 years Zoro for sure showed Ashura. This is head cannon assuming Ashura is the Conqueror. But Zoro has others fears similar to conqueror as his fight with Monet. Pretty sure someone like Mihawk with conqueror would realize that and teach him about it.
Mihawk wants to someone to surpass him. Initially would be Shanks. Maybe Shanks just keep up with Mihawk because of that. But Mihawk honor wouldn't accept to fight and lose to an one armed man. Mihawk then see in Zoro the same qualities Shanks has and expect to be surpassed by him. Oden and probably Ryuuma had greater potential by having Conqueror that Mihawk will never reach so he himself knows he can't be the strongest forever.