EU opponents demand national independence for their country, so that it can determine its own laws (e.g. on immigration, currency, defense, fishing) and conclude free trade agreements with all countries throughout the world.
On June 23, 2016, the citizens of the United Kingdom decided in an ad hoc referendum, promised by David Cameron, that the UK shall leave the EU (Brexit; 17.4 million or 51.9% of the voters). Since then, the country has been negotiating its withdrawal from the EU, wich, by decision of the UK Parliament, should have happened on March 29, 2019. The withdrawal agreement negotiated by Prime Minister Theresa May with the EU was more than once rejected by the House of Commons, leaving much uncertainty as to whether and when Brexit would be implemented.
The biggest obstacle to a true, constructive, mutually beneficial Brexit has been, on one hand, the EU's - in particular its Commission's - "arrogant intransigence", which denies any UK "cherry picking", to discourage all other member countries from following suit; on the other hand, the deep division in the British population and the fierce resistance of Brexit opponents, who dominate in the British parliament and government and who want to tie the country as close as possible to the EU.
The Brexit opponents are prophesizing total chaos and serious economic consequences for the UK, but to a lesser extent also for the EU, in the event of a disorderly WTO Brexit; the Brexiteers see in the PM's negotiated deal a Brexit by name only, the betrayal of democracy and the permanent submission of the UK as a "Vassal State" under EU dictate.
EU's opponents throughout Europe feel themselves affirmed that the EU has neither the will nor the means to fundamentally transform itself into a more democratic, subsidiary, decentralized Europe of the citizens, at variable-geometry (EU*), in which each Country can decide in an ad hoc referendum if it wants to participate in a politically integrated core EU, or in the common market (without euro and without the free movement of people) or in a large free trade area.
Are more Brexits looming?
The 27 remaining EU governments have supported Brussels' intransigence during the Brexit negotiations. Other EU member countries, that might try to leave the EU, will therefore probably have to choose either the "Chaos" of a "hard" Brexit under WTO regulations or the status of a EU "Vassal State" with a "soft" Brexit according to the "Brussels" -May treaty.