There is nothing wrong with the way he's being treated. They just made an alliance and people are acting like Mihawk is Buggy's underling or something. People are just shitting on him for the sake of it. Oda can't have Mihawk become a Yonko because that directly puts on in the PK wars, making him a target for Luffy and the other PK aspirants. Mihawk has no interest in OP. This is, like, one of the best ways to show us the guy's indeed a Yonko-level candidate without making him one.
It should be obvious for anyone with a half-working brain that Mihawk is the biggest reason why Buggy's got the title. Mihawk and Crocodile are literally the only people who we can even call proper fighters in this alliance, yet he was chosen as a Yonko over Kid and Law, who literally defeated Big Mom.