Siding with the yonkos in this one, specifically due to ranks and leaderships
Now I understand Mihawk never wanted to be a captain of anything but Oda only has Mihawk allying instead of leading, even with the warlords he wasn't leading anything but working under the WG
Now in MF war, there were 2 characters with the "Worlds strongest title" and only one of them lived up to the hype, which was Whitebeard (Leader of his own clique)
So despite there being another worlds strongest title holder, one looked much inferior and that was Mihawk
I'm talking about this..
Mihawk's slash was aimed at Whitebeard but the Geezer was smiling and got stopped by his underling (Jozu)
not only that, throughout MF Mihawk was just seen combating with commanders while WB and the Admirals were seen as the strongest in the battlefield
Now Mihawk is just an ally, not even a leader
Just out of pure speculation, Mihawk is nearly a big deal as big mom is, let alone the notorious Monster Kaido and Whitebeard