First things first. The opening monologue.
"Space, the final frontier."
I cannot and will not accept that monologue coming from NuKirk. Ever. Nowhere in this film did he show any ambition or intuition to be someone who actually wants to go out into the unknown and reflect what the monologue stands for. He went into this on a dare because he had nothing better to do, and his first goal was to finish the academy in three years. Why? Why does he want to rush through things? That's just counterproductive.
As for the topic at hand? Please. His authority in the Kobayashi Maru is the single most disconnecting moment I've ever had with a character. The whole premise of this test seems to rely on the notion that everyone involved, both students and trainers are the stupidest group of individuals who wouldn't know good commanding skills from a cockroaches attention span. Kirk is supposed to be leading his crew into a what seems like a losing situation, and he's just dashing their well put concerns away without even filling them in on what's going on. To make matters worse, when the simulation is over, he gloats around acting like it was nothing, and doesn't tell anyone how he did it or why. How are those good qualities in a Captain, let alone the hero of the story? Why would you leave your crew in the dark about a potentially fatal scenario just to satisfy your own selfish ego? If he was trying to make a point, why did he keep it to himself until he was confronted with it?
I can't believe people love his character. I can't find a single thing to like about him.