How is this "raw emotion", though? Leaving the EU has been discussed for a few years now, quite widely.
Also, "raw emotion", direct democracy (in Switzerland, for example) can work very well. Direct democracy may not scale well, hence we need representation, but big issues should be left up to the people to be voted on.
In the end, I believe, the people in the UK voted against not so much the idea of EU, but rather expressed their frustration with the EU's inability (unwillingness?) to fix its problems. It's been brewing for a while.
A big part of this vote is a huge swathe of voters who felt that they were not being properly represented by their representatives. All three major parties had similar lines on economic liberalisation, immigration and freedom of movement and so on and this has been the case for almost 20 years. So when a new party stepped in and said "we hear you, we want things to change to" it's not surprising it captured some of the public's imagination.
Remember the European Constitution that failed a few years ago? (At least the three hundred page document that they were calling a constitution.) I was shocked when my German friends mentioned that the German people would certainly have voted no, but they never got the chance. The German legislature voted for it, and that was it. Apparently most Europeans had no direct vote up or down for that constitution. And when it finally failed, it came from one of the countries that got a direct referendum.
But then thinking back to the US Constitution, it was voted in by the state legislatures without a direct vote, too. Somehow that seems OK back then, but an affront to democracy in today's world. How times change.
Even worse, many nations did not go into the EU by popular vote. Generally if people are asked about the EU, they don't follow the line of the politcal classes. This is just the latest example.
We elect politicians whose full-time jobs it is to understand big and complicated issues, and to decide on our behalf how to deal with them. That includes the right to make and break treaties with other world powers.
> We elect politicians whose full-time jobs it is to understand big and complicated issues, and to decide on our behalf how to deal with them.
But, on Brexit specifically, the British people elected a government that made a campaign promise to hold exactly such a referendum, and to abide by its results.
One very plausible theory I've seen doing the rounds is that the government never actually expected to have to follow through on that campaign promise. Strategically speaking it was a terrible idea and Cameron was always pretty pro-EU, but he needed the support of the anti-EU faction of his party, so he promised the vote as a sop to them. The theory goes that he didn't expect to get an absolute majority in Parliament and hoped the other parties would "force" him to to not follow through.
Otherwise, this happens.