That is a fundamentally incorrect interpretation of what a director does.

Then explain where my analogy fails.

Ultimately, due to how subjective the idea of art is there’s nothing I can say to convince you that this perspective is wrong.

You can change my mind by explaining how a director is different than what I've seen in hundreds of behind the scenes commentaries and documentaries on movie creation. To be more specific, some directors are also writers, storyboarders or cinematographers. But those are additional jobs that not all directors do.

because it’s so incorrect,

You need to explain why it is incorrect.