Well the thing is more Brits disagreed when we had a vote, and the outcome of the General Election that's just been held reaffirmed it beyond question.
It's called democracy.
That's funny Americans 'not understanding' Brexit when you're the only country in the world that doesn't even take the United Nations seriously. Sure you'd be happy to be run by Angela Merkel and a bunch of unelected clowns in Brussels.
Little wonder you don't get Brexit if you think EU is just about 'free trade'. If it was just about free trade, Brexit wouldn't be such a complicated mess. Something like 70% of UK's laws are (or were) made by unelected, overpaid, foreign bureaucrats.
Britain is not an 'international laughing stock' any more than it was when it decided to be the only country to resist Hitler against seemingly impossible odds.
Brexit might prove to be the most important geopolitical event in the 21st century if (as likely) it leads the ultimate break up of the EU (and perhaps the end of the trend of globalism submerging national identities).
Here's my two pence, as an American living in Europe. I think it will be worse for Britain than Europe, especially in the short term, but they will eventually forge new deals and adapt in the long term.
The first vote was heavily mis-informed (to be fair there was misinformation in both "leave" and "remain" campaigns), most famously with a false slogan about NHS on a double-decker bus. (I watched an interesting documentary about Cambridge Analytica that showed how easy it is to sway marginal votes, by identifying and targeting a small margin of "persuadables". They helped both the "leave" campaign and the "Trump" campaign.)
But you are right -- they re-elected Boris "the Clown" with an unexpected landslide majority three years later -- it is clearly what many people want.
One thing about Britain in Europe is that they never had both feet in Europe anyway, which no shortage of "except Britain" clauses, e.g. not adopting the Euro currency, and keeping the Pound. They consistently negotiated to have more of the benefits with fewer obligations. Of all the European nations who "gave up their sovereignty", Britain had the best deal.
The bigger problem with the initial referendum, besides the misinformation, that caused the transition to delay for so long, was that the people voting to "leave" did not share a common idea of what "leave" meant, nor did they give much consideration as to what the consequences of leaving would be when voting to "leave". As we have seen, the range of "soft" to "hard" Brexit options is almost as heated a topic as remaining was.
And the biggest problem of all -- how to manage the European Republic of Ireland border with the British Northern Ireland without violating the Good Friday Agreement. Erecting any kind of border between the two Irelands is feared to piss off the extremists groups, jeopardizing the recently established peace with a resumption of violence and bombing.
Bringing it closer to home (after all what do I care as an American who will remain in Europe?), my son has recently moved to London, and one of my biggest fears is if he will have enough to eat next year when all the European meat and produce is spoiling in trucks in long queues at the border. At least he likes ale.