Most people can’t be reached, of course, because you can’t reason someone out of a belief that he wasn’t reasoned into.
Apparently this venerable saying originates with Jonathan Swift. Is it true, though? How many of us form our bedrock beliefs through reason? None, I’d say. And yet how many of us change our minds later, whether grudgingly or willingly, upon being presented with alternatives? I’ve certainly reasoned myself out of ideas and behaviors that were impressed upon me early in life, and I’m sure I’m not unique in that. I think this is a case of the neatness of the rhetorical technique tricking us into accepting the truth of the assertion.