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In a nutshell: A tradition of Euroscepticism was amplified by the Euro crisis and the high-handed treatment of Greece, which further undermined trust in the EU's large powers (especially Germany), then 'austerity' happened (a word I don't like to use, as I believe it's a euphemism) and further increased inequality and dissatisfaction, a bad Act of Parliament was passed that set no proper framework for the referendum, and then in the referendum people were manipulated by means of outright lies like the £350m bus, and the 'remain' campaign was run extremely badly ('Project Fear').
Fundamentally, it's a combination of what some conservatives (small c) think about what should be the UK's place in the world, and grievances about the mind-boggling injustices perpetrated since 2010 especially, but also the spineless Blair/Brown governments that did not apply nearly enough corrective powers to undo some of the evils of Thatcher.
The reason why it's not so easy to 'take back' is because people (wrongly) see the referendum as binding and not advisory. This wouldn't necessarily be such a problem if (a) it wasn't also seen as a democratic verdict against the above combination of small-in-the-world Britain and injustice (by the respective groups, although they obviously overlap), making any suggestion to go back to 'business as usual' politically toxic, and (b) the UK hadn't been saddled with a hopelessly incompetent prime minister after the referendum, who obviously didn't exactly replace a shining paragon of competence (who immediately ducked out when he couldn't be bothered with cleaning up the mess he had created), but whose political mistakes like triggering Article 50 carelessly without any significant preparation, calling the 2017 election, etc. didn't help too much.
May I ask a stupid question please. I'm not British, but have lived in the UK in the past and Brexit intrigues me. I follow this thread and read the odd guardian article/analysis so know a tiny bit about what's been going on. Here's my question: wtf? Why? What's the idea? Why can't everyone (someone? anyone?) just shrug this off and say we're sorry, it was a poorly thought out idea, let's chuck it in the bin? Or rather, why doesn't anyone in government (I know lots of people do) seem to think that would work?