The captain insisted on finding Scott and the other crew members who had luckily survived first, then rescuing the abducted crew together. That way, they would return to the main storyline and outwit the villain.
It was the safer, more composed approach.
That was how the captain acted in the story: using every method available to eliminate danger, combining small tricks with great wisdom. His calm cooperation with the fierce Spock ultimately allowed them to defeat Krau.
Facts had proven this method highly effective.
But what did that have to do with An Yang?!
He could complete the mission while crouching in some ravine, and once the mission expired, he could still go home. If he followed the original plot, he would get nothing! Naturally, he objected.
The two launched into a fairly heated discussion.
Though one was a captain about to be promoted to Lieutenant General, while the other was merely an ordinary sergeant and security officer, the captain had just witnessed his strength. At a time when he did not even know how much usable power remained, he could only treat his subordinate with courtesy and hope to move and persuade him through reason rather than command him!
Yet after only a few sentences, Kirk discovered that he had been persuaded.
This stemmed from the asymmetry of information between them. An Yang knew everything about the story, while the captain did not even know the condition of the other crew members at this point, much less understand him. By concealing some information and deliberately guiding the conversation, An Yang could easily arouse the captain's sense of urgency, eventually making him resolve himself to act.
"Then let's do it!"
The captain's increased confidence and reduced fear likely also had something to do with the strength An Yang had displayed.