Re: "Kirk, You Do This, You'll Never Sit in the Captain's Chair Again.
Styles was an arrogant fop, but I see no reason to believe that he'd want an esteemed fellow captain like Kirk to ruin his career. I took it as a genuine attempt to defuse the situation before Kirk crossed the point of no return where he'd have no way to salvage his career.
From an out-of-universe standpoint, it served to punctuate Kirk's crowning moment of awesome a second later when he ordered warp speed without hesitation, and to clearly mark what was at stake and how far Kirk was willing to go for his friend.
My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away.