the/a white coach/black man's time.

[Ostap]

Here, Trevor Noah with his partner are discussing the uselessness of the Rooney Rule, on Trevor's show.
"Well, the problem with the Rooney Rule is that it underestimates racial bias. The Rooney Rule says: You don't like black people? Well, hang out with one and see what happens. But nothing happened. So now it's even worse, and you're still hiring the white coach and wasting the black man's time."
link with timecode

Hello! What meaning do both articles have in the sentence? Is it specific, or generic? Is it an imaginary setting where there is a specific "white coach" and a specific "black man" contesting with each other, and so "the" is used with both of them, or is it "white coach" and "black man" considered generally?

 

[SoothingDave]

It's a generic, imaginary anecdote, but the idea is that there is a specific "black man" and a specific "white man" who are both being interviewed for the coaching job.

 

[Tdol]

Just go with the flow- it's meant to be funny. And is.