The justification for "doing things differently" (e.g. leaving the EU) is that the UK is different to other European countries (in particular EU members). About 170 countries are not EU members. This makes EU countries, not the rest, unusual. They are more than unusual in name only. Among many other things, normal countries do not allow their legislature to be trumped by a supranational organisation.
(Moved from election thread)
Ah, but the UK is in Europe (the continent). That's the thing. Culturally, we are closer to other European countries than other parts of the world (look at the "Old World" shared history, the importance of social politics compared to say the USA, the similar architecture as a result of the shared history, the relatively good rail networks compared to other parts of the world, and good public access to the countryside, for example - all very "European" things). And geographically, we are very much closer. So really, it could be argued that we should be doing things similar to other (Western and Central) European countries as our cultural and geographical neighbours.
So if that is the argument, then really, we should be doing things similarly to other European countries.
I'm not saying there might not be other arguments for Brexit, perhaps - but these are not relevant to this particular discussion. Most arguments for Brexit (sovereignty, controlling the borders) would be valid arguments for other countries to exit the EU too. And I certainly don't want to get into another argument about immigration; that's not the point I'm trying to make.
The argument that somehow we are not "like" other European countries while all the other western/central European countries are all similar is hard to comprehend. For one thing, it assumes that EU/Schengen countries are one homogeneous bloc which we are somehow very different to. Why are Bulgaria, Estonia, Norway, Iceland, Ireland, Portugal, Cyprus and Germany all culturally similar to each other - but the difference between us and any of them, including Ireland, is greater than the difference between all those EU/Schengen countries?
And don't say "island nation"! Ireland, Iceland, Malta and Cyprus are also island nations, with Ireland and Iceland in particular more isolated from the mainland than we are.
Doesn't make sense. Yes, there are significant differences in culture between different European countries but I don't understand why the UK is more different than the rest of them.
The Celtic nations of Scotland and Ireland provide a particularly graphic example. Is the cultural difference between Scotland and Ireland really bigger than the cultural difference between Ireland and remote parts of the EU?