EU opponents are demanding national independence for their country so that it can decide again on its laws and conclude free trade agreements with all countries of the world.
They believe that the present EU has neither the will nor the capacity to thoroughly reform itself and to create a more democratic, subsidiary, decentralized, flexible Europe at variable geometry, defined and supported by its citizens.
In such a Europe, each country could decide by referendum if it wants to participate in a politically integrated core-EU, or in the European Common Market or in a vast Free Trade Area, open to all European countries between Vladivostok and Reykjavik.
EU opponents therefore want their country to leave the EU. This is the position e.g. of the United Kingdom Independence Party (UKIP), who claim that the British Parliament in London can hardly legislate any more, since the vast majority of its laws are decided in Brussels.
London is also forced to apply them without ifs and buts: the UK cannot, e.g., control immigration like most other countries in the world can do, nor can it sign free trade agreements, not even with countries of the Commonwealth, such as India, Australia and Canada.
Conclusion: If all countries followed the EU opponents, the European Union would be reduced to a - politically not integrated - common market or a European free trade zone, a Europe of nation States cooperating mainly on the economic level.