When people use it they are not really thinking and using the most accurate language, but instead using a rhetorical heuristic, a mental shortcut where you hyperfocus on X and ignore Y.

It is reflex and often it is not useful to argue with people about the reflex for they will get defensive and not understand why you are critiquing their language choice. Not realizing they are not persuading but merely arguing for the cheap seats for the people who area already half sympathetic to the language choice. Arguing with them on the choice of the word will trigger "Reactance," a form of motivated reasoning for they feel you are restricting their choices even if the language they are using is not accurate and even often half chosen without forethought or afterthought but instead merely as a mental reflex.

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Note all humans, including myself have much language where I too use mental shortcuts, rhetoric heuristics, and not use true critical thinking or accurate language in conversation all the time. Some of the time I am "present" and some of the time I am not. This is the case for all humans.

This is the nature of humanity for heuristics are shortcuts and it is less cognitively draining. It is something that humans and animals merely have evolved much like pumping blood in a certain way where arteries and veins do different things.

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As for how this language idiom developed it is a long story with not 1 part of the story but dozens of small things (small stories) that created this term via a process of gestalting. Aka it will take a chapter of stories to explain how the two word idiom

"Liberal Media"
or its variant
"The Media"

developed. It is not rational / logical it is an organic term like much of language is.

• I can tell you some of the stories such as the 1974 and 1978 elections and the rule changes with media / congress. How congress itself changed the rules of how media could cover congress with the goal of sunlight and how this actually did not create sunlight but insteadperformativeactors in congress. Actors who pretend X is happening when reality other things were happening. Aka the art of creating narrative by looking at X and ignoring everything else.
• The moral majority rise in politics. This moral majority used to use similar language at other ills of society but now reorient the similar language now at the media and so on. Saying the media is not covering the true issues.
• The Fairness Doctrine and the removal of The Fairness Doctrine.
• The economics of broadcasting but also how the broadcasters were concentrated due to economics but also limited radiowave space due to physics and technology we used to be limited on for decades.
• and dozens of other stories. Stuff I am not even bringing up here.

I am not going to explain the origin of the term for I do not have time, and I will also be leaving things out and it will be better to learn the origin of the term from multiple sources and multiple points of view.

I trust you Legolas if you are still curious about this term that you can find the history from multiple sources and become more familiar with the term in the United States. But my point I want to leave you at the end of this rant above, is that language is not always logical / rational / etc and we (not just you and me but everyone) needs to accept that language is not purely logical. Language at the same time is both beautiful and stupid. Afterall...