The EU appears to have been too complex a subject for many voters to fully understand, and there was allegedly widespread distrust of the "experts", leading to large numbers basing their decision on emotional responses instead, such as "I don't trust the experts so I'm going to do the opposite of what they recommend" and "I like this bloke who talks about listening to the 'little people' and 'taking back control'".
I know there are some people who voted Leave for well-thought-out reasons, and that I can respect, because it is rational. But most analysis suggests the majority who voted Leave did not do so for rational reasons. In which case it is like cutting off your nose to spite your face. And it is not as though this was a local or a general election - this has made England and Wales look very bad on the world stage, and is something we're all going to have to live with for a very long time.