Absolutely it's difficult for everyone. But the difference is that educated people have the tools to think objectively, abstractly, and logically about their "quirks, knee-jerks, assumptions, [and] opinions."
For example, take progressive taxation. Understanding progressive taxation as it affects me is simple. Understanding progressive taxation as it affects people like me is only slightly harder. But there can be no real objective understanding of progressive taxation without understanding concepts like, but not limited to, what John Rawls' called "the veil of ignorance."
There are plenty of people who stand for and against progressive taxation without understanding the veil of ignorance, but their understanding of it is either subjective or simplistic, no matter which side they're on. They do not have the tools to truly understand their own position, and thus they are not equipped to support it, to refute the opposing position, or to recognize if and when they're wrong and think about exactly how and why they're wrong. If one is unable to do that, it is much, much less likely that one will change his mind on a subject. And even when one does change his mind on a subject, his new opinion is going to be worth about as much as his old one.
It has become fashionable to claim that all opinions merit equal respect, but it is simply not true. The opinion that is grounded in objectivity and logic is superior to one that is grounded in emotion and subjectivity, at least insofar as the consequences of the opinion in question, as social policy, affects others, like him and unlike him. (In other words, someone's emotional attachment to Mandy Moore and thus his opinion that Mandy Moore is a better singer than Billie Holiday was doesn't really matter.) The only thing sacred about opinions is that everyone has the right to hold and express them; that right of equal expression does not translate to equal value.