And this error is ironically an illustration of the exact problem he was commenting on: our brains tend to work by association, and implication (A implies B) tends to be interpreted as association (A implies B means A and B are associated, which means they go together, so A implies B is a way to say B implies A).

Ah, good ol' modus moron, as Angelo Margaris's "First Order Mathematical Logic" calls affirming the consequent.