I don't want Mihawk to be anything; I am just not stupid and think like Oda "accidentally" gave Imu the same eyes as Mihawk in the Manga, had Mihawk constantly refer to other people as rabbits, insects, etc., which, as we now learn, is very similar to the Gorosei, and if we want to be real for a second,?
Just look at Yoru for crying out loud. It is literally the World Government symbol turned into a sword!
Now, how and why Mihawk will be "related" to Imu is entirely unclear. He could have a situation that mirrors Shanks. Mabye, he is not blood related to Imu but got adopted or found. Maybe he is an Imu clone. Maybe he is just Imus's son. Who knows but Oda at at the end of the day?
Besides, who honest to God gives a shit? Mihawk has a dead or alive bounty poster, and unlike Shanks, Mihawk has a history of not working with the WG and refusing to listen to them to such a degree that it is clearly noteworthy when Mihawk actually shows up to Marineford and throws an attack at all.
Mihawk is not secretly going back home to chat with the Gorosei "about a certain pirate" like Shanks did, so he is not a snitch. Also, to be blunt, nobody actually thinks Shanks is weak for talking with the Gorosei, okay? Nobody sane thinks he is weak. It's a slander meme on the level of black paint, Mihawk. Or, rather, I hope nobody is actually stupid enough to think Mihawk painted his sword.
Agenda Piece has just rotted many collective brains to the truth. If ANY other character had like a fifth as many hits to be connected to Imu, that shit would already be established fanon, and nobody would even question it. And before anybody says, "Does that mean Mihawk is not a self-made man?" no, likely not because when has Oda EVER made such a character?
Like, all agenda aside, every other world's strongest is either par of a special race or at least heavily implied to be (Buccaneer, Oni) or has a stupidly strong fruit. But Mihawk is going to be the WSS, perhaps even the strongest swordsman ever prior to Zoro, without any fruits and no special abilities of any kind while also not being in any way part of some special family line? That does not make any sense.
Oda does not write characters this way, whether people like it or not.