This is a typical case of inadequation between the expected benefits and the perceived ones.

The topic is complex, and an in-depth explanation of it would probably not suited for the scope of this site. However, some elements might help you grasp an idea.

Conflicting Goals

The problem when you do a revolution, is that you typically agree that the guy who's there is bad. You all work together to get rid of him. But once that's done, you often fight amongst yourselves, because you never took time to find a system for afterwards. French revolution, or even Lybian revolution (for somethin more recent) come to mind.

The EU has a bit of the same issue. With 3 "large" wars in 80 years (Prussia-France followed by the two World Wars), involving progressively more people and killing exponentially more people each time, both the leaders and the people of European countries felt like something should be done. But what?

People often expect the EU to spread humanist views, favour human rights, environment, peace, etc. So we would all be living better, to make sure that will share the best standards in Europe. We all live in peace, like each others, so won't be waging wars again.

Some other, and among them many industry or polical ledears, are more focus on economy-oriented. A shared market, leads to a shared economy, increased inter-dependence, and thus impossibility to do any total wars. And making some profit on the way won't harm much.

From the very begining, the EU has been a ship trying to compromise between those approaches. The 1957 Rome Treaty claimed to be adressing the former, whereas the first actual agreement, merged the coal market.

During the Cold War, the EU was building and expanding itself, but partly as a way to protect itself from the USSR as well as keeping some independence from the USA. The USSR disappeared, the memory of the World Wars faded, people started to evaluate what they had built.

Many feel that the EU is too administrative, and retraints the free exchange and market. Others that the EU is too business oriented and not doing enough for the Human Rights, Environment, and general protection of the population.

Complexity

To put it simply, the EU has three institutions:

• the Parliament
• the European Court
• the Commission

The Parliament is directly elected by the European people. People can somewhat understand that, as it is quite common in the national systems as well. It holds legislative power.

The Court is somewhat separated, but holds judicial power. This entity often exists in one form or another in each country.

The commission is a complex and puzzling entity. It holds both executive and legislative power (often avoided in separate countries). It is composed for a part of the representants of each member countries, for a part of nominated people.

That complexity makes it hard to follow who takes which decision and who should be held responsible for each new rule. And that puzzles voters.

Communication issues

There is a huge communication issue for the EU. Except on very rare cases, the EU does not promote itself so much.

Whenever there is a debate on national politics, you would see representants of the both sides in all news medias: radio, TV, press, etc.

But you would rarely see the same thing whenever there is some debate at the European level. A a French, we regularly get to hear Muscovici (current European Commissioner for Economic and Financial Affairs, Taxation and Customs) on media, but most of the time he is being asked about national politics rather than European ones.

I don't know if it's a question of consumer's interests, journalists, or EU officials, but the result is that for a large portion of the population, the EU institution look like a black box, completely separated from the "normal" people.

Even national politicians communicate the European decisions sparingly and only to achieve national goals.

Populism and xenophoby

More or less latent since the 1970s, we live in a continuous "crisis". That crisis has many facets: economics, moral, societal, technological, etc. The economics part of it exploded since 2007.

People are by nature resistant to changes, and thus somewhat preoccupied about the future. And whenever we are in a crisis (or simply perceived to be in), we tend to look for culprits. Jewish for example, have often been considered culprit (Geman's loss at the end of WWI, a few economic crisis in the Holy Roman German Empire, etc.). It tends to unite a population against the culprit.

This is something often used by extremist parties. The rise of polpulism isn't something specific of Europe. The famous "Make America Great Again" of Trump is a clear illustration. The crisis is due, for some people (or presented as such), to the globalization, world economy and multinational firms. Thaose are many heads, and hard to focus the hatred against. In Europe, the EU institutions are an embodiement of those. So by focusing the distrust and hate against the EU, those parties capitalize on the fear of many people.