The EU consists of many zones that unite countries: the economic zone (biggest), the EU and the Euro zone. The latest 2009 crisis and the recent Brexit revealed however how fragile and un-united the EU is compared to other federal unions.
1. Historical and cultural differences
In history, Europe has always been divided in different nations with closed borders. That made travel and cultural exchange difficult. A french still feels french, a German German, … The US was also populated by many nationatities, but they had one dream in common: getting a better and new life and a new nationality
There are now already 24 official EU languages. That doesn’t make communication and a united feeling easy. The US only has to cope with Spanish and English (to my knowledge).
In schools, children get a national education, but certainly not a Europe directed one. And even national feelings are not so strong. Imagine singing the European (or even the national) anthem at a concert or other public occasions (aside from sport competitions). Unthinkable in Europe and people would even find it ridiculous. Almost as normal as saying hello in the US.
The EURO was a good step in making life easy when traveling and paying. In the beginning only countries with a strong economy could participate. Later “poorer” nations were allowed. The big crisis that affected Greece, Italy, Spain, Portugal and Ireland showed again division. The fact that the “rich” had to pay for the debts of the other was not helping a united feeling. This seemed to play less in the US between states.
5. Power and money
Maybe the most important. Although we have a European parliament and government, every nation still has its own and even subgovernments (belgium is specialist in that). This is for so called protection of the national interests. But it is more clear that all the local politicians don’t want to give up their well payed jobs, networking and are power gay. The US could start from almost scratch when it was founded, so new structures were not fighting that much with existing.
And there are many other reasons, but these are the most important to my belief.
And it's interesting to know from other “unions” how they cope with their “united” feeling (Russian, Australian, ...)