It is conventional to give people the benefit of the doubt—to err, when possible, on the side of uncertainty and not to presume the unlikely is untrue. But it is one thing to give the benefit of the doubt in uncertain circumstances, and it is quite another to give an outsized benefit with very little doubt indeed. That, in essence, is origin of false balance.
Worse, of late the media has taken to determining what subjects are in doubt not by what evidence is available, but instead by how forcefully people argue for one side or another. A forceful but untrue statement often triggers a confused and muddled response from journalists, who, by dint of their profession, know both that the statement is painfully untrue and that to contradict it outright is painfully taboo.
Journalistic conventions, intended to ensure fair treatment regardless of personal inclination, fail abysmally when public figures refuse to play by the rules.
There are things you can say in polite company, and things you can say in private; we all know this, and yet we profess shock upon hearing publically those things we deem for limited specific company only. But it isn’t the sentiment we reject, it’s the form: we have an entire structure of polite register that allows us to express private sentiments publically, but less directly. That is, after all, the structure of formal English—to say with euphemism and evasion those things we could say bluntly with a more limited audience.
There are a bunch of people out there right now who want to tell you “support the police” and “blue lives matter.” Many of these people also say slightly more nuanced things like “there is more crime in black neighborhoods so police are needed there” or “there are 
As usual, the debate about academic freedom 
Political correctness is one of those things that conservatives love to hate. Understandably; there are few areas where people can indulge in righteous disdain and still maintain broad support (instead of just looking like jerks). And why not? There aren’t many people, I think, who enjoy being on the receiving end of the language police. It’s understandably infuriating to be told that you said whatever you said the wrong way, even though your meaning was obviously clear.
Trigger Warning: this is a post about content notes and trigger warnings. People who become irrationally angry when they encounter content notes or trigger warnings may want to stop reading now and spare themselves the emotional distress.