There are plenty of reasons, not that I have a strong belief that Shanks is stronger but I've seen quite a few arguments.
There's the idea that by becoming a Yonko, Shanks surpassed Mihawk by hype and portrayal. Doesn't really prove anything as a Yonko can be a swordsman and Shanks being one doesn't automatically make him stronger than Mihawk as it's a position not based solely on individual strength but influence as well.
That Mihawk's title doesn't apply to all who wield a blade and the idea that Shanks may utilize something we have yet to see and him potentially being reliant on whatever that is, instead of simply his blade makes him more than simply a swordsman. Not getting into that one since it's something people can't seem to agree on and I see why. But even if we look at it this way, it doesn't outright prove Shanks is stronger.
Because Shanks is who Luffy aspires to surpass and Mihawk is who Zoro aspires to surpass. Again, doesn't prove that Shanks is stronger.
Some people find his feats underwhelming and too few but that's understandable for a dude so strong that's reserved by the author for one of the MC's. Plus, his iceberg cutting feat was crazy. Shanks' feats are also scarce, he has the sky-splitting one when he clashed with Whitebeard. There's also stuff like him ending the war but I wouldn't say anything at the end of Marineford proved he was outright stronger.
The idea that since Mihawk never surpassed Shanks when they dualled, perhaps Shanks didn't get weaker after losing his arm and Mihawk's belief in that is unfounded. Again, isn't really a "Shanks is stronger," argument but more of a "he isn't necessarily weaker," one.
Overall I'd say people really like Shanks. I, personally don't worry too much over who's stronger between the two since I like both though I perfer Shanks and I'd be fine with either being stronger than the other but I'd lean more towards Mihawk being stronger based on what's in the manga and what we're aware of like his title and due to the fact that there isn't much you can use to argue Shanks is stronger. Though, due to what little we know, Oda proving the notion that Shanks is stronger isn't impossible. At best, we can say Shanks might be stronger and that Mihawk is simply unaware that Shanks is so strong. Pretty much due to how mysterious Shanks is, people could see him busting out some game-changing stuff.