Two people are caught in some highly compromising situation, and one says to the other: “Think of something quick!” Why is this funny? It captures something about the human condition—there were surely lots of times in our evolutionary past where the ability to think of something quick was a vital survival skill. We should not be surprised to find that humans are endowed with an excellent ability to make up explanations after the fact. We should not confuse the ready generation of explanations for motivation with actual understanding of our motivations.
The argumentative theory of consciousness is similar to The Interpreter Theory in proposing that the function of consciousness is primarily verbal (and therefore social). While the interpreter theory explains puzzling neurological evidence, and is plausible from an evolutionary perspective, the argumentative theory goes farther by explaining puzzling evidence from cognitive science, social psychology, and behavioral economics, especially relating to the phenomenon of cognitive biases.
In short, the argument for the argumentative theory is primarily that the human mind seems well suited to generating persuasive arguments (stories) and not so well-suited to unbiased rational decision making. In particular, the notorious Confirmation Bias insures that information that supports our position is easily recalled, whereas useless opposing evidence rarely comes to mind unless we make a strong effort to recall it. Another form of evidence comes from how people change their decisions when they know they will have to justify their choice. People then often make worse decisions because they choose actions based on how easily justified they are. See Arguments for an Argumentative Theory.