What does Les say people need to be convinced of?
People must be convinced that their old Adamic nature is a natural-born rebel against the things of God. The carnal mind, still under the control of old Adam, is enmity against God, and even those who claim to love God remain rebels until the gospel operates in their lives.
Les explains that verse 7 throws a curve at most people, because the carnal mind—anyone still under the control of old Adam who has never had the gospel operate in their life—is enmity against God. People insist they love God and are not His enemies, but the book says they are, and it doesn't lie. Their old Adamic nature remains a rebel, and a rebel is an enemy. That is what people must be convinced of: their natural-born rebellion against the things of God. Les also notes that this truth rests on the absolute reliability of Scripture, which has foretold events hundreds and thousands of years in advance, all coming true.
Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.