In this particular example, Pharrell pointed out the red herring which Blake uses with many artists, his background as someone who lived in Nashville and various other "typical country" towns. Instead of explaining how he would help the artist improve to eventually win, Blake focuses on the close living proximity of the artist and himself, using this as the basis of his argument. In retaliation, Blake uses post hoc, demonstrating an over exaggeration of Pharrell's famous, big hat, he states that since Pharrell wears something as silly as the hat, it is impossible to take him seriously as a voice of authority.
There are many other moments from The Voice demonstrating logical fallacies. While this may not be the most elaborate or best suited example, it is extremely memorable which is why it stood out to me when thinking of what to write this blog about.