Khan had walked into the club knowing that the situation wouldn't have been in his favor, but Rodney had only needed a line to show how bad everything was.
Monica had already educated Khan on that topic, so he found it easier to accept the situation. Rodney came from a wealthy family. He had received social and political training since birth. He was probably below Khan in terms of adaptability and cunning, but those types of conversations were his reign.
Khan felt cornered for obvious reasons. He didn't have any leverage, and Rodney knew basically everything. The specifics of Khan's mission might escape his knowledge, but they weren't important now.
Silent seconds went by as Khan tried to find a way to turn the conversation in his favor, but Rodney's stance had no flaws. Khan couldn't defeat him there, and only one move could create a crack in an otherwise helpless situation.