It's my understanding that politicians on both sides of the argument agreed to put it to a vote. If that's wrong, then correct me.
The politicians who opposed Brexit thought it would never pass the vote, so they let the vote happen. Then when the vote went against their will, they have not changed their direction in accordance with the public choice.

It's that misdirection that I find ominous.

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I still believe that the (shifting) majority can choose to vote again, though. I agree with your argument against setting the precedent, but I think we're not alone in that. I think that if the majority opinion has changed, then that's fine. It's each society's prerogative to change as it will. If it has changed, and there is popular outcry for another vote, then it's only democratic to hold another vote.

Forcing another vote from the top down is not OK with me, but if it is called for from the people, then I think you have to admit that is, in fact, democracy in action.