One purpose of the Inciting Incident, and another reason for it to be separate and distinct from the Call to Adventure, is that it establishes polarization between the Hero and the Antagonist or Greater Antagonism.
For example:
In The French Connection (1971), the Inciting Incident establishes Pierre as the bad guy and the context of heroine export from France to the USA.
In Star Wars (1977), the first sequence introduces the Antagonist and the need for a resolution [Vader kidnaps Leia].
In Little Miss Sunshine (2006), the first sequence shows us Olive watching the beauty parade. This Inciting Incident establishes the distance between plain old Olive and the possibility of her winning such a competition (polarization).
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