And ordinary working people believed them. And the intelligent who wanted to remain were incapable of putting forward a sufficiently convincing argument to persuade them otherwise.
That a democratic debate and vote goes against your strongly held view is not some kind conspiracy - the success of the Brexiteers is a reflection of an inadequate Remain campaign.
I think there is another dimension to this that isn't being aired here:
I disagree that there was not a "sufficiently convincing argument" from Remain - the details were absolutely crystal clear - all of the negative things that have happened were predicted and evidenced.
The other factor is that the Leave camp pursued a deliberate campaign of lies and deceit. Alongside this were the "Brexit Aligned" press, who desperately wanted Brexit for their own aims and profit - and broadcast the lies and deceit even though they knew it was a lie. And alongside all of that were the Social Media Echo-Chambers where the people who had swallowed the lies - mostly because they
wanted to believe them and
wanted the outcomes they were lied to about - and were singularly not able to entertain the "opposing opinion", despite the mountain of credible evidence that supported it...
Finally, alongside and supporting all of that - the deliberate lies, the deliberate precipitation of the known lies, and the entrenched partisan Echo-Chambers - alongside all of that was the social media Bot Accounts (funded and supported by shady sources such as the Kremlin and Tufton Street) flooding those Echo Chambers and empowering the entrenched partisan followers to deny the evidence mounted against their views. Those bot farms disappeared very quickly after the referendum (but have also been used to equal effect in the recent US Election - and again the activity disappeared very quickly after the Election).
^^All of these things were actively pursued by the very wealthy, in pursuit of their selfish aims, and targeted the least well educated in society to vote against their own best interests.
And alongside all of that, the ghouls of the Brexit Press were active in pursuing what they nick-named "balance" from all other media outlets, including the BBC - but this was definitely not "balance" - and instead simply a counter-argument based on known lies - and insisted that this pack of "known lies" was also propagated by the "responsible" media, threatening to call them biased if they did not meet with the blackmail and represent a known lie - which was the "opposing view".
I think that covers
most of it.
Sadly, the least well educated cannot accept that they were lied to, even when they discover they were lied to, and deep down know that their opinions are based upon known lies, because human nature is a fickle master. People are known to dig their heels in even when their views are demonstrably based upon an easily proven falsehood. The most well educated are more likely to accept the evidenced view and allow the facts and truth to guide their opinions.
If you feel uncomfortable with the above paragraph, you ought not to, because it is a very well evidenced field of research, and if you try to refute the body of evidence supporting it, that basically signals a pre-existing bias and an unwillingness to accept credible facts and truths. Which is poignant, don't you think?