It has everything to do with it, others dont get to do what MC does.
Nope. Chapter 997, if you read it, says that Zoro is targetting Kaido.
If you missed ch 997, several others have also shown Zoro targetting Kaido.
But 997 is crucial to tell you why Zoro is targetting him.
On the other hand, you know all of this but choose to play dumb.