What is being objected to most is "ever closer union", and, more particularly, the speed which which this is being pursued by the unelected Commission. If the time scale for that were some hundreds of years, during which time everyone got used to everyone else, that might be a worthy goal. As it is, it's just being thrust down everyone's throat by people who cannot be gotten rid of. And people don't like it, as witnessed by the growth of "anti" parties all across Europe.
People in the richer countries are fed up with bankrolling the poorer ones, and the poorer ones just view the richer ones as a source of free dosh.
We have to walk carefully away, because it will end in tears.