James T Kirk explained in 3 sentences, ladies and gentlemen.
It’s very interesting to me that Kirk actually begins his career as a command officer firmly in the square of lawful good. He’s a rule-follower. He believes in the chain of command. Comparatively, Spock is much more of a neutral good character throughout the series: he will do things by the book when he thinks that will do the most good— which is often, otherwise he would not last long in Starfleet— however, when he feels disobeying the rules is the more moral choice, he does it without hesitation. But over time you watch Kirk’s frustration with those occasions where the chain of command fails, times where he makes the ‘correct’ choice and it doesn’t work, times he pushes his orders to the absolute limit, crossing boundaries to do what his instincts tell him to do. And it makes him question things more. He and Spock are alike in that they both believe that there’s no such thing as an ‘acceptable’ loss, if that loss is a fellow officer.
This is Kirk doing what he knows he has to do in order to honour Spock’s wishes after his death. The only thing. He stands to gain nothing— and lose everything, because he understands that he will be court martialed and stripped of his command— but in his mind he’s already lost everything. Spock is gone, and they’re retiring his beloved ship. The only thing he has to gain at this point (because he doesn’t know Spock’s body has been resurrected), is the knowledge that he’s doing the right thing. And the choice is really as easy as it is in the frames above— because he knows it’s the choice Spock would make in his place.
