…And Justice For All
The purpose of an improvised lecture on the benefits of libertarianism is to change a person’s perspective. After that, they can rewatch any films—whether from the beginning or from scratch—that touch upon the relationship between power and the individual in any way, and see everything in a new light.
Unfortunately, I don’t know of any films that provide a sufficiently accurate representation of a society under ancap. One would have to search thoughtfully to see if there is anything interesting about the stateless period of the Wild West, or the gold rush in Alaska, or if the mischievous Japanese have created some anime about ancap that is more plausible than Cowboy Bebop, and so on.
Sometimes libertarians tend to recommend something moralizing about how vile the state is, and how it particularly unpleasanty stepped on someone’s toes in a specific case. I don’t know, I’m not a big fan of direct propaganda; I find it more interesting to root for the Trade Federation in its entirely justified pursuit of secession from the Galactic Republic than to listen to pompous monologues from the adaptation of “The Fountainhead” (though Gary Cooper is a handsome man, of course!). And in general, it’s more pleasant to notice small details in passing than to be attacked directly; the latter is more likely to cause rejection.