Archie is interested in spreading evil throughout the school.  He chooses The Goober for an assignment because he is untainted and good.  Archie can't resist the chance to corrupt this goodness, and he chooses the perfect assignment for him.  By requiring The Goober to unscrew the furniture in Room 19, Archie is symbolically unscrewing The Goober from his moral foundation.  Archie has detached The Goober from his goodness, and replaces it with deception (of Goober's parents) and shame.  Once The Goober realizes what he has done, his corruption is complete.  This is why he wants to quit the football team (Ch. 23), to cleanse himself of his connection to Trinity and to regain his lost goodness.