One view of the European Union is that it is a cooperative venture by countries who agree that they have much to gain by working together, perhaps analogous to a tennis club. An alternate view is that the EU is an empire, and that countries which have joined to the now in some sense "belong" to the EU. (This model has much in common with some early modern theories of the social contract, according to which once one surrendered one's sovereignty to the king one forfeited the right to resist if he abused the power he had been granted.)
The language of EU politics is for the most part more in line with the "tennis club" model. That said, I don't think that the "empire" model should be immediately rejected. The EU does a lot of genuinely worthwhile work in preventing various member states from being a lot worse, particularly the members in southern and eastern Europe.
The biggest problem with the empire model is that it is completely unpalatable to the man on the Clapham omnibus. We don't want to believe we are owned by a bunch of people in Belgium!
One difference between the models is how they will treat people attempting to leave the EU. If someone decides to leave your tennis club, then you may be saddened but you will not obstruct their leaving and you will wish them well. By the empire model, however, for a country to leave the EU is for it to wrong the EU leadership, to betray its master/owner.
A lot of behaviour over the last month - not only by the EU, but also by a lot of its supporters (example) seems to fit much more into the second category. That, I think, is a fundamental disconnect at the heart of the EU debate: many (though definitely not all) pro-EU people follow the empire model, while Brexiteers are uniformly people on the tennis club model who either believe that the time has come to pack in that membership, or who realise that the EU leadership adhere to the empire model and don't like where that train of thought leads you.