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The biggest problem Brexit faces is that so few people, on the UK side, actually know what they are talking about.
For example, the talk of reciprocal rights for EU citizens here vs. UK citizens in Europe is incredibly difficult - not just the "knock for knock" style debate that is being put forward. This is because (generally speaking) the UK imports working age people, and exports pensioners - treated very differently under EU law.
So, to take this example further - healthcare is provided to UK pensioners in the EU, because the UK is governed by EU Regulation 883/04 - which attempts to harmonize/integrate social security systems around the EU. This means that the Member State which pays your state pension, also covers the cost of your healthcare - regardless of where you live in the EU. Stay with me here! So, if the UK is no longer governed by Regulation 883/04, then there is no vehicle to pay for our pensioners' health costs. Fine, you all say, so the UK then agrees a bilateral arrangement with Spain whereby we continue to pay Spain for providing UK state pensioners with healthcare. Simple, right? But then why Spain? Why not Thailand, Australia, the US? Indeed, why do it at all? Why should tax payers subsidise pensioners living in abroad? See what I mean? Lots to come out in the wash and simplistic, generic statements/arguments will no cut it.