Luffy and even Buggy the bombastic clown are bigger rivals to Shanks currently than Mihawk is
Every pirate in the sea is a rival for the One Piece.
That doesn't mean shit.
This nonsense doesn't mean much really, rivals like Whitebeard and Roger attack each other on first sight, meanwhile Mihawk and Shanks are simple friends who shared something in the past and that's about it, they didnt even fight each other for whatever reason. Each one has his own business, Mihawk is only interested in honing his swordsmanship, meanwhile Shanks was bred to one day carry Roger's legacy to the best of his ability, literally the biggest legacy in the story.
I posted 2 canon sources almost a decade apart, both of which called Mihawk & Shanks "Rivals".
You: "That doesn't mean much"
I'm sorry but there is nothing to argue here.
If you term Roger & Whitebeard as "Rivals", then Mihawk is the one who should be Shanks' rival. Heck, one of those sources i posted even compares Shanks/Mihawk to Roger/WB in terms of their relationship.
They canonically competed in Legendary Duels.
His rivalry with Teach existed since they were once kids, and he's the man to give him the most memorable of scar, a scar significant enough that it characterized the jolly roger of Shanks' crew. These two are tied by destiny since birth
They aren't Rivals, this is like saying Xebec is Roger's rival and not Whitebeard.
You are missing the point, BB has been fated to clash with Shanks but they aren't competing for anything except the One Piece - which they are also competing for against Millions of other pirates in that case.