I really didn't read anything personal into Styles behavior. Sure he was a bit arrogant about it, but it didn't seem like he was jabbing Kirk personally more than he was very pleased with himself and his ship.
The warning about never sitting in the captain's chair again... is just that. It's not that Styles is going to personally take away Kirk's command, but that Kirk's about to commit himself to an action that will lose him his command. If I tell my friend about to commit a crime, "If you do this, you're going to go to jail." It's not that I'm going to personally drag him down to the jailhouse and lock him away, but that he's crossing an irreversible line with his own choices and actions.