Of course, this is not a 100% truism. My height is 5' 7 1/2". It is rather easy to prove that I am not 6' tall even were someone were to claim such. Obviously, in this case I can easily produce evidence/facts to prove I am NOT 6' tall.
Where proving a negative is impossible is when there is neither evidence nor facts to back up an assertion.
"Assume we are friends and I invite you over for dinner. After the meal and after you have left, I discover that a small, valuable antique is missing. So, I accuse you of taking it. You respond with 'I didn't take it'. But, I don't believe you; so, I tell all of our mutual friends of my suspicions.
There is no way you can "prove" you didn't take the item - even though you did not. It's impossible!
The analogy of the above example is what we see running rampant across the political spectrum today.
Both Hillary Clinton and Donald Trump, almost daily, face accusations and allegations emanating from "anonymous sources" with no actual facts in support. The allegations against Clinton do not get the same level of coverage as those against Trump. This is mainly due to the bias of the progressive media outlets; these outlets far outnumber their opposites.
The vast majority of such allegations are without proof or other merit. This puts the receiver of such accusations in the unenviable position of trying to prove a negative - an almost impossible task.
Let's look at two examples: "People working for the Clintons have a way of going missing or dying - at the hands of (specifically) Hillary Clinton." and "Trump colluded with the Russians in order to help him get elected."
The first of these two examples, "People dying around the Clintons", is not a 100% conspiracy theory - That scores of people working for the Clintons have gone missing or have died is a fact (Click Here and Click Here). That Hillary Clinton, however, is responsible is an accusation that is without merit or proof and falls under "Proving A Negative Is Hard To Do". How could she ever prove she was NOT responsible either directly or indirectly?
The above story has gotten little or no traction from the main media sources due to 2 things: 1) The factual portion of this story does not fit into the politically progressive narrative; and 2) Truly responsible media sources have no facts to support that Hillary Clinton did anything untoward - NONE in this regard!
The second example, "Trump colluded with the Russians in order to help him get elected.", is a whole different story as far as the media goes.
Almost hourly we see all media sources reporting on this allegation - with both positive and negative connotations from progressive and conservative media outlets alike. We are bombarded with this despite the fact that there is NO evidence or facts to support the allegation.
So, Trump, his staff and his family are constantly put in the position of trying to prove a negative; i.e., Neither Trump nor his team had any illicit/illegal contact with the Russian government - which can't be proven.
Such allegations as exampled above seem to follow Valdimir Lenin's infamous quote: "A lie told often enough becomes the truth." If people hear a lie often enough and don't bother to verify it's accuracy, after a while perception becomes reality, as it were - to our collective detriment.
Further, such allegations also seem to fit in nicely with Saul Alinksy's "Rules For Radicals". If we look at these "rules" objectively, we can see them being applied across the political spectrum; especially rule #5, rule #8, rule #10, and rule #11 - again, to our collective detriment.
Politicians and the media love to throw out factual-sounding statements which, in fact, are what we like to call "fake news" these days. Take, for example, this article I did on a speech Sen. Elizabeth Warren gave to supporters. Her comments were totally disingenuous.
A suggestion or two:
Whenever words/terms such as "from an anonymous source", "it was reported that...", etc., are used, a WARNING FLAG should go up. Check it out. It's is probably fake news.
Whenever a statement is made sounding as if it is fact confronts you, when offered without substantiation or source, check out the veracity of the statement. You may find that the fact stated is anything but.