I don't want to encourage resparking this topic, but I'll answer this one post in a fully informative tone as someone who believes in Mihawk's strength.
Reasons why people believe Mihawk is top tier or at least stronger than Yonko who wield swords:
1. MIhawk was given by Oda the title of "World's strongest swordsman" because of that title, anyone in One Piece who wields a sword is by definition inferior to him in strength.
2. He was rivals/had various duels with Shanks prior to 10 years ago when Shanks was not a Yonko, but once Shanks lost his right arm, Mihawk decided to not duel him anymore because Mihawk had no interest in fighting a one-armed person.
3. He is Zolo's end goal to defeat, therefore he MUST be Zolo's end of series opponent and by manga definition, whoever is EOS villain/opponent must be insanely strong, stronger than anybody faced before them.
4. If I am missing anything else, please let me know.
There are many flaws behind this reasoning.
I'll tell what you're missing,
in my opinion. But I want to highlight that I don't want to enter the Mihawk vs Shanks discussion and I'm only making this post to inform of why I personally believe Mihawk can be that strong, so you, and anyone else who reads this, may hopefully understand why some of us believe in this, even if you don't change your mind.
- Mihawk's only narrative purpose to the story, the whole point of his character's existence: if Shanks is stronger than Mihawk, then Zoro won't achieve his dream until he defeats Shanks; the stronger swordsman. Mihawk's sole existence in the story is to serve the purpose of being the personification of Zoro's objective. Becoming the strongest swordsman in the world, by itself, is a very blurred concept. How do you have Zoro prove that? Defeating Shanks, Big Mom and everyone else by himself? Would that still really prove it? Perhaps Rayleigh is stronger, or that Gorosei with a blade, how do you give the readers the satisfaction of eventually seeing Zoro achieve his dream? Making a personification of his dream, someone who already is the strongest for him to defeat: Mihawk. If Mihawk is not that strong, he has no purpose, and actually immediately becomes a much, much worse character by failing at the only thing that gives the character meaning.
- Mihawk's vivre card.
People claim vivre cards can be wrong, but there's nothing to indicate that it is, and the example they pull to say vivre cards have been wrong about something important before was that in Shanks vivre card they accidentally messed up the order of two events in a timeline. That kind of error is very different to making up a whole paragraph on a character, and the vivre cards have introduced trustworthy canon information before, so I don't doubt it without good reason.
I only highlighted the paragraph where Shanks is mentioned, but all of the above paragraphs are equally interesting, like he becoming famous before Roger's execution and running out of worthy challengers. Related to that, I'll also say that we have no information on why Mihawk and Shanks stopped dueling. The whole one-armed thing is an assumption from what could just have been a friendly taunt.
In any case, this is just my interpretation, but that particular paragraph sounds like Shanks is still the greatest challenge in Mihawk's past to becoming the strongest and he wishes someone even stronger will appear in his future to give him a thrill.
And I'll make it a different point, but the paragraph about him sailing freely is another reason why I trust Mihawk.
- Mihawk's lack of crew.
What makes a Yonkou a Yonkou? First of all, they need to be pirates, secondly, they need to be incredibly powerful (though there
are people who can give them a challenge other than other Yonkous), and finally they need to own BIG chunks of territories in the New World. All Yonkou's crews are big, some more than others, while Mihawk hasn't got a single crewmate, and this has many implications.
1: Even is Mihawk was stronger as a duelist in a 1vs1, he would still be weaker as a pirate. If Mihawk got into a fight with Kaido or Big Mom, he would get overwhelmed by their crews whether he wants it or not. No matter how much stronger some characters are compared to fodder, big numbers are always depicted as significant in the series, and it's not like all Yonkou Commanders are complete pushovers.
This makes Mihawk powerless when speaking about "piracy" regardless of his individual strength which is why he's not brought up when talking about the pirate's summit. He's barely a pirate, in reality: he has no jolly roger and no interest in the One Piece.
2: Without a single crewmate or even a ship, Marines considered him dangerous enough and feared enough to make him into a Shichibukai instead of just capturing him (like they will attempt now with their new superweapons). The other Shichibukai (except Law, who took a hardcore path to get his position) had pretty dangerous crews to back them up, like the fish-man pirates, the kuja tribe or the Donquixote Family.
3: As a Shichibukai, he's despised by most pirates, who consider them dogs of the government. However, Mihawk has been freely sailing all alone through the New World and Yonkou territories for the 20 years since Roger's death.
- Mihawk's bounty.
Shichibukai's bounties didn't mean much over the course of the series. All of them were supposed to have become much stronger over the years after having their bounties frozen as Shichibukai. However, the first Shichibukai to be introduced to the story is the only one who hasn't got his bounty revealed yet. This doesn't mean it's gonna be the highest we have ever seen, but it does seem like Oda is saving it real good. Now their bounties have been unfrozen, so it's gonna be very relevant again when it gets revealed.
And I think that is all, other than the most obvious point of all: Mihawk is above anything Zoro shows before they fight.
