> A leave voter would argue for exactly the same thing - a clear majority need to vote to remain.
But that's exactly what I'm saying is importantly not symmetrical. Making major changes has extra costs beyond the advantages and disadvantages of being in one state or another.
There is a symmetry here, one you remarked on earlier, but it maps the Brexit referendum not to itself with roles reversed but to earlier EU-related decisions that were made without referenda. You could absolutely argue that, say, signing the Treaty of Maastricht was a major change that the individual states involved shouldn't have made without consulting their populations. I'm not sure I agree -- see below for why -- but it's definitely the same sort of issue as with Brexit.
The reason why I'm not sure I agree is that the entry of the UK into the EU was done gradually. The UK joined the EEC (without a referendum at the time, but there was one a few years later on whether to stay, which a large majority voted for, suggesting that joining without an explicit referendum was maybe a reasonable step), which was a substantially less major change than joining the EU would have been if it had existed then, and then the EU gradually increased its scope: Maastricht, Amsterdam, Lisbon. The combined effect of all those things was large, but each individual step was smaller, less risky, and (maybe) more undo-able.
(I do think, on balance, that probably each step should have been subject to referenda in the countries affected, with rejection triggering a rethink of how much European integration to aim for how quickly.)
If the proponents of Brexit had been able to divide Brexit into phases, each much smaller, less risky, and more undo-able than the whole, then that would have had many advantages and the downsides of a simple-majority referendum would have been less, though they'd still have been big changes and I think should still have needed more than a bare plurality of votes. I don't know whether any such thing could actually have been done, and kinda suspect not.
> If a majority vote isn't a majority vote [...]
Not every vote has to be a majority vote. Being a democracy doesn't mean that at every instant you do what The Majority wants at that instant, no matter how slimly it prefers that. Not because there's anything particularly wrong with The Majority, but because like an individual it may change how it feels too often for that to be a good idea.
(Likewise, having my own interests at heart doesn't mean that at every instant I do what I want to at that instant. That's why we have things like marriages and contracts and deliberately-established habits. My preferences are noisy and benefit from a bit of low-pass filtering, and I think the same is true of almost everyone. So we deliberately get ourselves into commitments it takes some effort to get out of. We can still get out of them -- you can get divorced, quit your job, explicitly break off a friendship, etc. -- but it's to our advantage that those things aren't so easy to do and we will only do them when we are really quite sure that they're a good idea. I think research suggests that most people are a bit too reluctant to make such changes, but the amount of friction we want getting in their way isn't zero.)
> What was the well-defined outcome of the UK joining the EEC in 1973? [...]
I am bemused by the question because I never so much as vaguely hinted that there was any such thing. I said that in 2016 the option of staying in the EU was a well-defined one with known advantages and disadvantages, unlike the "leave the EU somehow but no one's specifying any details at this time" option it was opposed to on the ballot papers.
I completely agree that joining the EEC in 1973 was not like that. That too was a major change, though a smaller one because the EEC was a smaller deal than the EU became over time, and holding a referendum on that (with something more than a mere plurality being required to proceed) would probably have been a good idea. As I said above, the result of the referendum held not long after suggests that joining would probably have won by a comfortable margin, in which case holding a referendum wouldn't have made much difference -- but as a matter of principle I'm in favour of explicitly running such things past The People unless it's already very clear what they want.