There is no confusion and this thread sucks.
It is pretty simple. Mihawk just wanted to check the true distance between them and Whitebeard. And what happened? Jozu showed up to protect papa. And when Kizaru tried to attack him it was Marco. And this is no different from when Ace was trying to meet him and had to face Jinbei first.
This mean that by having a chance to fight the big guy you first need to pass by his subordinates.
And the other way around is true. To get to Admirals, and Garp and finally Fleet Admiral, Luffy had to pass by a bunch of marines, Shichibukais etc.