John Wilkins comments on an old fable, often attributed to William James, in the service of commenting on the snooty attitudes toward common folk beliefs ("Turtles all the way down"). The anecdote in question is well-known enough that I need not recount the whole thing (I think I first encountered it put to humorously literal effect in a Terry Pratchett book).
These anecdotes serve to legitimate the narrative of the teller of tales, to show they are on the right side of history, and to lessen our appreciation for the ordinary person. And they are pernicious. The weak minded have failed and we strong minded have succeeded, and history was always moving towards this point. This is the positivistic narrative of Comte: society has shrugged off the superstitious and theological and achieved enlightenment. Except that it is a lie.
I am glad that Wilkins points out that these stories are intended to make the benighted look stupid -- often an exercise in kicking the powerless while they are down.
In both versions of the story (also told by Stephen Hawking, whose literary and historical skills re not so good as one might think, given how often he is quoted authoritatively on this subject), the flat earther is a member of a despised and ridiculed group – blacks and old ladies – and in both they stand in for the stupidity of the folk belief and believer, overcome by the truths of science.
I hate it when I encounter (all too often) this snooty superiority attitude. Great comments after the post so far, including Nick Matzke finding an instance of the story from 1856.