Otherwise, this happens.
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.
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.
Why should something like this be any different?
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.
I'm sort of jealous. They had a referendum on Scottish independence and they honored the outcome. I'd love to have an up/down national vote on abortion, gay marriage, gun background checks.. At best here in the US, you're voting for a derivative, you're electing someone on the wish/hope that they support your issues if they get a chance or opportunity to of if they're willing to use political capital to actually propose the issues.. With something like abortion, it's at least 2 derivatives removed, you're voting for someone who will hopefully select a court justice (should they get to) that will align with your issues should the opportunity ever arise for them to make a judgement on it. And what's more perverse, there are a lot of single issue voters that take that multiple derivative issue situation as the only issue that matters.
It'd be an interesting experiment if nothing else.
It's possible to get readmitted, but only with the consent of every single member state.
Britain always pushed for more liberalization. See where it led them. They were able to push for what their GDP needed, alright.