I think its fairly easy to make a case of why the EU is a bad institution. I have made so here and other places. I think people are blinded by the idea of the EU but ignore the actual EU. Can anybody deny that the EU has shown horrible management in everything related to economics? We have a Great Depression level crisis and now a horrible slow recovery. 90% of this hole crisis could have been avoid if the EU and specially EMU were such horribly setup institutions. The EU is not really democratic either, when it should be the most democratic. It should improve on the state of institutional democracy, while in reality its a very clear step back. Take a look at Swiss Federalism and Direct Democracy, its a much better set up for a system but many of the ideas are nowhere to be found in the EU.
Britain has economic problems right now because a lot is changing, but I see no reason that the long term growth should be negatively impacted by this. In the long term I think it can be a net positive. It all depends on how Britain will operate going forward.
Only 37% of the population was needed for this, but this is because the UK voters had been apathetic about the opportunity to reform the voting system.
So how can they claim to be disappointed by the EU adopting the same polities?
The UK has a reason for their bad system. They have a very gradualist history. Compare it to France, where we are talking about the Republic 5 right now.
If we are doing a project for European Unity is should actually be better then everything else. It should be better then Switzerland, not worse then the UK.
Of course many people voted because they want to "close the borders" but: 1) This doesn't invalidate the sovereignity argument. 2) The protectionism/anti-immigration stance is a reaction to the existing politics, not the cause. And it's something we currently see all over Europe.
There are more valid arguments for leaving the EU, but I think the argument for democracy is the most important one. Saying there are no good arguments to leave is dishonest or ignorant.