Whilst Leave won the referendum, I can explain why Remainers consider that they have an opinion and input to the prospect of leaving the EU with a comparison:
Imagine for a minute that the vote had gone the other way.
How would Brexiters have felt if Remain had won by 52 – 48, and Cameron had taken that as a mandate for greater integration with the EU, and had spent the last 2 years joining Schengen, adopting the Euro, promoting the idea of a European army and a federal Europe, etc?
Would you have accepted the loss of the pound and the introduction of the Euro and said ‘well, we lost, better get over it’ and ‘the people have spoken – it would be undemocratic of us to continue our criticism of the EU’?
Does anyone, from either side, seriously think the Leave camp would have just shrugged their shoulders and not felt entitled to an opinion on further integration?
Or would you be saying “It was a very narrow vote, the matter is far from settled”.
Would you be pointing out that the referendum only asked if people wanted to stay in the EU – not how they wanted to stay, not ‘hard remain’?
Would you be angry if the votes of yourself and the other 48% of the voters were being entirely ignored, and the only thing the Government seemed to care about was the other 52%?
Would you feel that remaining was a terrible decision, that ‘project fear’ had swayed the result, and now a government was claiming a 100% mandate, on the strength of 52% of the vote (37% of electorate & 26% of population), and following a course of action that profoundly damaged the country?
Would you feel that you were not even entitled to hold an opinion about the Euro, and that you should have no influential input on its introduction?
If you can spend a few minutes imagining that scenario, then you will have the answer to the question.