The European Dream got crushed by neo-liberalism
Essentially, the dream of a united Europa got crushed, because Europoliticians are ever more clearly and openly dedicated to defending the interests of banks and corporations (OWO) rather than of its inhabitants, favoring business and economics (with secret treaties like TTIP) while paying almost no attention to social and human values as they did initially, while those values actually constituted the essence and identity of Europa, at least for its citizens. However, this clash between citizens and corporations is not a European problem; it is the greatest serious globalized problem (leading to most other problems, from wars to climate change) and it has its roots in neo-liberalism.
It is through neo-liberal politics that banks and corporations have gained growing control to manipulate and corrupt politicians all over the world, including indeed and sadly the Europoliticians who have now greatly become servants of big industry & finance instead of being enganged leaders of their citizens.
The generalized argument of BREXIT advocates is that the United Kingdom (quite an arguable OWO definition in itself) would loose its 'sovereignty' if remaining in the EU and they point to the, indeed, rotten politics of our Union. What they don't explain is that ALL countries and citizens are equally suffering this increasingly rotten political model and that it does not have anything to do with national borders or being either or not part of the (any) Union, but that it is the globally generalized and growing conflict between normal citizens and, again, the banks and corporations brought about by neo-liberalism.
The British brought neo-liberalism to Europa in the first place
And neo-liberalism was introduced in Europe and propagated by Britain (Thatcher) in the first place. Most probably the British share of neo-liberalism is proportionally larger and stronger than from any other European country. So even if the British get their 'sovereignty' from Europa, they will simply drag along their own part of this rotten global system and business will go on as usual for British citizens. Maybe it will actually become even harsher under a 'sovereign' UK because the compensating forces are weaker in the UK then they are in the EU.
More sovereignty for Europa!
At the same time, this means for the remaining countries of the EU, that thanks to a BREXIT Europa will actually be freed from probably the strongest and most aggressieve neo-liberal, corporate and financial lobbying machines within the EU. Without the pressure of London's stock exchange and City, European politics will have more air, space, strength and indeed sovereignty to regain at least some of those social and human values that we have been loosing over the last three decades since the outbreak of neo-liberalism. The British desire and 'need' to regain 'sovereignty' will actually give back more sovereignty to the European institutions and citizens than to the UK itself.
Increased European cohesion
With much respect, and feeling sorry, for the average British citizen who cannot oversee the manipulation they are embedded in, a BREXIT would be actually the greatest gift the European Union could possibly get in these complicated and troubling times for all world citizens. Being rid of the nagging, strong and aggressive London manipulation, played out through lobbied British politicians, will increase the chance that the EU can fight with more succes their own lobbied politicians, who are the true cause of the aparent scattering of the European Dream. European citizens, movements and non-neoliberal parties will find more steady ground to bring back politics to its one and only role: represent the citizens. This will allow the EU to become more powerful, not based on industry and economics, but on humanity and social values. This 'softer' side of the EU will ultimately prove to be its greatest strength and might well become an example for the rest of the world, if true Democracy and social Justice get the chance to grow and flourish for once and for all.
As says Paul Degrauwe spot on: "When Britain (London) will no longer be able to undermine the EU's cohesion, the EU will come out stronger."
British nationalism great reference for European reconstruction
This documentary, "Brexit, the movie" that advocates the 'United' exit of England/Scotland/Wales/northern-Ireland out of the EU, is fantastic! Most arguments are correct, although they don't just describe a British problem regrarding the EU as it currently exists (in fact no more than a "Union of European Countries, Politicians and Several Other Entities", some not even European) but a general problem of all European and World countries, more specifically its citizens, caused by their respective neo-liberal regimes.
The British go about it with a very old-fashioned and obsolete, kind of pre-WW II, nationalistic view, maybe because many of them (unconsciously?) still cling on to those old glory days of their 'Empire'. The rest of Europa fortunately does not carry this burden. So once Britain has left, the people of the remaining EU countries together can intensify the fight against the true cause of Europa's decline (the neo-liberal regime, introduced by the British in the first place) instead of just walking away from some superficial symptoms. Many of the arguments in this video will be applicable.