The "big lie" term was coined by Adolf Hitler in is book Mein Kampf, and refers to the propaganda technique of (an authority figure) telling such a huge lie that the audience just accepts it because they cannot fathom such an authority figure telling such a blatant lie, and thus assume that it must be true.
A more popular form of this, put forward by Joseph Goebbels, is that if a lie is repeated enough, it becomes true (in the sense that people at large will simply start accepting it as true without question; it becomes true in their minds, even against evidence of the contrary.)
This is actually understandable from a psychological perspective. We are pretty much hard-wired to believe in things that everybody else believes. If everybody around us believes something, without question and without criticism, without alternative views, we tend to take it for granted as well. This especially if we have been raised in such an environment all our lives. It requires an unusual kind of skeptical mind to doubt that belief. Unfortunately only a small minority of people have this talent, and they are usually ignored (and sometimes even shunned) by the majority.
When that belief is actually accurate and conforming to reality, there's no harm in it. However, the harm may come when the belief is actually not accurate and differs from reality. People may start acting according to the belief, misled by false information.
The infamous "wage gap" is such a big lie. It has been repeated over and over and over during the past decade or two (and in increasing amounts during the last few years), so much that many people just take it for granted, without question, without skepticism. Anybody doubting this self-evident "truth" is ridiculed and shunned, called names and insulted. You see this "fact" being repeated in a very matter-of-fact manner by people, including celebrities and authority figures.
There is, however, a relatively easy way of countering the claim: Just ask for an actual, concrete example. Ask for an example of an actual specific company that pays less hourly salary to women than to men for the exact same job. After all, if the claim is true, there must be thousands and thousands of companies out there doing this. Coming up with one single example shouldn't be that difficult.
Every time this subject has come up, online or offline, I have asked for such an example. So far I have been given zero of them. People just repeat the claim as a self-evident fact, but never have a single actual example of it to give. They just believe it with no factual evidence to support it.
Be aware, though, that as always with these kinds of things, some smart-ass might actually give you a concrete example. It will probably be fabricated (but there's obviously no way to prove that on the spot), or it might even be true, who knows. But there's a perfect answer to it: "Have you reported it to the authorities? Paying women less than men for the exact same job is illegal."
Note that not all types of job are the same. Not every job is that of a factory worker, where the person checks in at 8am, does exactly 8 hours of work, doing some mundane repetitive task at an assembly line, and then goes home. Not every one of them is a desk job. Or cleaning toilets.
Some jobs are creative, and are based on talent and skill. Some people may be more talented and skillful than others, and might be much more proficient and outright better at doing the "exact same" job. There may be "supply and demand" in play here; not of physical goods, but of talent, skills and knowledge.
Sometimes it might not even be a question of talent and skill, but just of fame, when we are talking about a public figure, like an actor, or a speaker. For example, two actors may technically speaking be equally talented and qualified for a role, but one of them is a world-famous celebrity actor who will draw in the masses to movie theaters, while the other is a completely unknown nobody just fresh out of drama school. The world-famous actor (or rather, his agents) will ask for more money than the unknown nobody, and will refuse to take the part otherwise. It's then up to the produces and executives to decide which one they will hire. (In this case, it's actually the "worker" who is demanding a higher salary, and refusing to do the job otherwise, rather than the "employer" just paying less for the "exact same work". It's up to the employer to decide which one they want.)
Fashion modeling is another perfect example of this. And, curiously, an example where the "wage gap" benefits women more than men. Top female models are largely paid vastly larger sums than top male models, technically speaking for the "exact same work". Again, it's a question of supply and demand, and a question of the "workers" demanding a certain salary or refusing to do the work otherwise. The more famous and popular models will get higher sums than the unknowns. The models that draw in customers and viewership will get higher sums than the ones that don't.
Or take another example: Anita Sarkeesian (at least some time ago) had a speaker fee of something like 20 thousand dollars. If I, a completely unknown nobody, were to offer myself to speak at the exact same event, do you honestly think that the organizer would be willing to pay me 20 thousand dollars, even assuming they would even accept me as a speaker? They might be willing to pay me a hundredth of that sum, if even that. Is this a "wage gap"? Or is it a question of supply and demand? A question of which speaker will draw in more listeners (and thus more profits for the organizers.)