The thing is, there are loads of legitimate reasons to be unhappy with the EU. That's the case with any union. One of the more compelling ones I have heard is that the EU has always been essentially a federalist project, and the UK has always been one foot in, one foot out. Incidentally, I don't think this argument is that compelling because there isn't enough political capital in the EU at the moment to begin pushing for federalisation. Even if federalisation was impending, it would have to be passed by the parliaments of the member states (for which there would likely have been a referendum, to which the UK could say no).

People are insulted and defiant about being called wrong, even in the face of a mountain of evidence.

This is an important point, I think. I've had some luck with the Socratic method when it comes to things like evidence-based medicine - essentially having a collaborative discussion with the other party to tease out underlying assumptions, leaps in logic, and so on (my mum is into alternative medicine, and I am a biomedical scientist so that drives me up the wall). The key thing is to make it cooperative instead of combative so as to prevent the other party from digging their heels in and getting defensive. It also helps to improve your own reasoning, of course.