I think what happened is some people simply believed the half stories being told by politicians, it's quite shameful they were allowed to do it, but the remain campaign was there to try to show the other side.
So for example, so many focusing on the 39 billion a year. Yes it's a big number, but it's not the whole story. As the the net benefit to us, is approx £3000 per year per household, so it's akin to paying a penny to get a pound back, but the campaign only focused on the penny, it never told about the pound, and when the remain side tried to explain it. They were shot down as scaremongering. The result is people like the pp thinking they are parasites, when in reality what we gain financially far outweighs what we pay.
Another example is the wto terms, how hundreds of countries trade on these, How we can trade on these, but they failed to mention every single one of those countries has supplemented it with their own trade deals. We would,literally be the only country in the whole world trading on only world trade terms.
So many half Stories, people not looking at both sides, working it out for themselves simply believing what some politician says, so you see them, rubbing their hands in glee, thinking yes, we will have 39 billion more, which is less than 0.5 percent of our gdp, but not realising we will actually on average be 3000 pounds per household worse off net by coming out.
Because literally we pay a penny to get a pound. So now we will be grasping our pennies, whilst the world looks at us like we are total idiots.