The problem is framing. For example, Trump once said "There were very fine people on both sides." regarding Charlottesville. This is a fact. However, he also went on to say "The white nationalists should be condemned totally" when asked for clarification less than a minute later, indicating he was referring to the pro- and anti- statue removal protesters as very fine people, while excluding the white nationalists (and probably antifa). That part is completely ignored and to this day large swaths of people believe Trump was endorsing white nationalism in that speech, even the neo-nazis themselves, because left wing media selectively presented the truth.
You may be an expert on left wing media; I'm not. All I can say is that I've seen both parts of that quote reported in places I'd consider "left" leaning, as well as more centrist like NPR and the BBC. Hearing the second part doesn't change the fact that Trump clearly didn't feel it was necessary to criticize white nationalists until he was pressed to take a stand, and then he said the most politic thing. The fact that he didn't shout it out the first time says a lot about Trump right there.
The first part by itself is more "newsworthy", however... and you'll find that media left, right, and center always emphasize the juiciest bits. That is a valid criticism of the media in general, but also a reflection of the modern audience's limited attention span. I wouldn't be surprised if some of the same venues I referred to also reported the story in a briefer fashion that excluded the second part.
How would you even word a rule to prevent such things?
Interesting question, but why are we talking about media coverage of the news, anyway? You brought up "left wing media", something certain people like to complain a lot every chance they get... but the original story is about advertising on Facebook, and the comment you replied to was talking about posts (often ads), presumably also in the context of Facebook.
So I'll address your question as if it was on that topic: I think it's true that there's no perfect rule to eliminate distortions of the truth in ads by omissions or quotes used without the full context, and even if there was, every politician does it, so you'd have to ban political ads altogether. Truly not a bad idea, and most of the audience that Facebook is selling would love them for it. Except Zuckerberg wants the advertisers' money, and it's also very difficult to define what's "political". Better to go ahead and take the money, but for christ's sake have some standards!
Because, as the GP pointed out, there are some things that can be factually determined to be true or false. However, because of the reason you point out, framing matters. But even things that are not as simple as true-or-false can be adjudicated to be excessively misleading. Misleading quotes taken wildly out of context could and should also be fairly banned.
In addition to banning objective untruths, Facebook could have a rule along the lines of "Factual but misleading quotes are not allowed, IF the average person's interpretation of the quote would change if they saw the quote along with any other comments by (or words written by) the same person, in the same context, around the same time, or in the same written work.". The legalese might be more painful; that's just pseudocode.
Could they do it without being seen as biased in the court of public opinion? I think they have a duty to try, but they must set up an independent panel that reviews all complaints, and that panel must make all its decisions, and its decision-making process, completely public. Those interested in seeing the controversial ads could still see them, along with all the accompanying discussion and judgement. But they wouldn't be pushed by Facebook as paid ads to the intended audience. Then, if you think your ad got banned unfairly, you bring it to the court of public opinion. Make a big stink about it on Twitter that gets Donny's attention, or get your favorite fair-and-balanced media outlet to raise a stink for you, and then people can seek out the ad to see for themselves the evidence for why it didn't pass muster. Maybe they'll agree, maybe not. But if you, as the one who tried to buy the ad, feel you're standing on firm moral ground, go nuts and reap the benefits from the "any publicity is good publicity" when your ad itself becomes the news. Yay for you!
My point is, while it's difficult to be fair, and not everyone may agree, keep everything open and you're unlikely to face criticism from anyone reasonable. And being a private company, the first amendment doesn't enter the question. Unfortunately what matters to Mark Zuckerberg more than any single other thing is money, and any hope that he'd feel a sense of duty to encourage truth in politics is... completely laughable. He clearly doesn't care where his money comes from.