On the error of failing to appreciate your opponents' three-dimensionality:

They had cliche answers but only to their self-created straw-men. To exaggerate only slightly, they had never talked to anyone who really believed, and had thought deeply about, views drastically different from their own. As a result, when they heard real arguments instead of caricatures, they had no answers, only amazement that such views could be expressed by someone who had the external characteristics of being a member of the intellectual community, and that such views could be defended with apparent cogency. Never have I been more impressed with the advice I once received: "You cannot be sure that you are right unless you understand the arguments against your views better than your opponents do."

Source: Milton Friedman, "Schools at Chicago," from The Indispensable Milton Friedman

H/T David Henderson at EconLog

Note: The final sentence of the passage, as presented by Henderson, is missing closing quotation marks. I have added them.