The Wormhole wrote:
Because he didn't change his uniform until after he boarded the Enterprise. Here's
an image where he clearly has Captain's stripes.
I hadn't noticed that.
I don't think that there'd be a situation where Kirk voluntarily accepted a demotion to Captain, just to be promoted again for Trek 2. Perhaps he had a temporary reduction to Captain for the time he stayed in command of the Enterprise, then later, when the Enterprise was assigned as a training ship in trek 2 and Spock took command, Kirk went back to his old job and went back to Admiral. After that he never officially had command of a ship again until Trek 5, by which time he was captain again.