It's the honesty of the situation. Claiming it's because it's undemocratic when really it's about what it actually does is quite disingenuous.
It's no surprise that those who generally support what the EU does don't see a democratic problem, whereas those who don't think it's an authoritarian dictatorship (at the extreme end of opposition).
Democracy is all about the individual relegating his/her personal beliefs to those of the population as a whole. It provides a means for those opposed to a situation to know when they are defeated.
I wanted Zac to win the London mayoralty but I accept that the majority of Londoners did not and I wish Sadiq well. I accept that the correct 'demos' for a vote on the mayoralty is the population of London. That demos spoke and my view was in a minority.
Likewise I accept that the correct demos for a vote on nationwide UK matters is the UK, and I will accept the views of the UK population expressed at the next general election.
That said, my personal belief is that mayors and local councils are about the most democractic institutions we have, and we should be devolving much more decision-making to local democratic institutions.
Some of the anti-democratic arguments about the EU revolve around its institutions. But, in my view, what most people really object to is the demos. It is harder to express this view without being branded as 'Little Englanders'.
But the point is that democracy only works when people are happy to postpone their own views behind those of the majority of the demos. If the demos is cast too widely for a particular issue, then people feel that their voice has been diluted too far, and that the decision-makers are too remote from them.
The EU does not, in my view, restrain itself to only those matters which really must be decided on a continent-wide basis. It neutralises national innovation and competition. It plays only lip-service to the treaty principle of subsidiarity.
Ironically, part of the reason why the EU institutions are not wholly democratic is out of an acknowledgement of the demos problem. We can't have a sovereign European Parliament without a European populace which is happy to share in a full federal democracy.
This does make a sustainable democratic European Union a bit of an 'all or nothing' approach. I suspect that you would be happy with a fully federal United States of Europe. That is an honourable view. I would prefer a friendly inter-governmental association of sovereign countries. I think that is also an honourable view.
I don't think that the third option, muddling along with the half-half approach, is going to be sustainable for the UK or for other European member states. But because of the assumed toxicity of the federalisation option, we're only being offered Brexit or muddling along. I choose Brexit.