Possible Clues:

• Plausible but fallacious argument
• Thus Greek character's beginning to make specious argument
• His poems, not English, needing translation? That's a poor argument
• Contained in Aesop, his morally false argument
• Bribe the chap's missus initially? That's a fallacy
• Thus political leader conceals his faulty reasoning
• Specious argument
• Work during break, caught out in fallacious argument
• Thus top politician conceals his deceptive argument
• Faulty argument