Something about how Jim became so accustomed to Starfleet parlance that it’s the only parlance he can speak at all. Something about how his relationship with his ship and his work as Captain extends to language as well, to the way he handles and expresses his emotions.
Amok Time – Kirk is confronted with the fact Spock keeps a dangerous secret that, if not shared, might end up with his first officer killed
The Apple – With the landing party marooned on a strange planet and the USS Enterprise being pulled ever closer to the ground, Kirk asks Scotty something beyond excellence.
The Doomsday Machine – Commodore Matt Decker stands in the maw of a monster with a dead crew and stripped of any will to live. Kirk tries to bring his old friend to reason, but nothing else can be done for Decker as he looks death in the eye.
I understand how, especially in the third instance with Matt Decker, he might've seemed cold (your buddy is about to off himself, and you remind him the higher-ups spent too much money on his formation), but I see it more as Kirk trying to ground both himself and his friend (who is also a Commodore, might I remind you) than simply reducing Decker to his position.
It also accidentally reveals a lot about Jim (although reveal is not the best word, as that same thought has been explored in numerous episodes before), how much his sense of worth is tied to his job—to how well he can perform and excel at it.
But that's not all he's saying. In both instances (Amok Time and Doomsday Machine), Kirk puts himself in the Federation's place because he sees its recognition as more valuable, more "worth living for" than his own.
It's his way, the way of a man who knows no life other than that of servitude, of saying I care about you, and I don't want to lose you.
It's really tragic that it is not enough to save Decker. If both Matt and Jim share the belief (which appears more often than not in Starfleet overachievers) that your inner worth is tied to how well you can perform it, Matt is left face to face with the rather morbid fact that he failed severely and his whole crew is dead because of it.
To sin is human, yes, but if the Doomsday Machine is the Devil, as the Commodore himself put it, it truly is a shame Decker did not view himself as deserving of forgiveness