Because the most sustainable, successful, stable form of government is the nation state.
No foreign superstate is sending my kids to die in a war EVER, not happening.
Laws and decisions of that nature should be taken by a government that is elected by and is accountable to the people.
1. What power do you have? 2. Where did you get it from? 3. In whose interests do you exercise it? 4. To whom are you accountable? 5. How can we get rid of you? (with thanks Tony Benn).
It's a simple question of national sovereignty. That is the objection.