"The media" are not a monolith. Or at least they weren't until recently when right wingers began buying up every damn thing.
The main point here is that neither the FCC nor any other arm of the government should be able to dictate what the media say about them. Trump (and by extension, Carr) think they're special and should be insulated from criticism. Questions and criticisms are exactly the media's role, and they always has been. The media are there to put a check on government corruption, excess, tyranny, misuse of power ... whatever word you want to use here.
Every time Trump says to a reporter asking a question about his actions, "you're a terrible reporter," he is attempting to abuse his authority to intimidate the reporter and invalidate the very reason the media exist. He cares not one whit for the first amendment. He knows exactly what he's doing, because he has always been a bully and a thin-skinned putz. There is nothing more un-American than bullying reporters.
Jesus Christ, Jeff. Gimme a fucking break.