Can anyone point to specific scenes or lines of dialog to support their opinions?
For instance, one interpretation could be that Spock began to respect Kirk during their argument about the Kobiashi Maru. But that could be just me reading into the scene my preconceptions based on prior knowledge of Star Trek.
Also the initial scene of Kirk and McCoy on the shuttle gives an impression that they share a bond. What that bond is isn't clear. But the movie jumps forward in time to a point when they are friends and doesn't really show how the become friends or show the basis of their friendship.
What in the movie shows, to the uninitiated, Kirk and Spock (and McCoy) becoming friends.