The plot to leave the EU (I was going to say 'plan', but there is no 'plan', so 'plot' will have to do) is shit. Therefore it is BrexShit, and will remain so AFAIC. I care not one jot for the feelings of the small minority of madmen/madwomen whose votes have brought us to the brink of disaster, despite there being an overwhelming majority of the electorate who did not vote to leave in a seriously-flawed referendum that was only ever intended to be advisory - a 'finger in the air' to test how the wind was blowing. If those of us who wish to remain are 'Remoaners', I reserve the right to refer to those who support leaving as BrexShitters.

As far as the referendum was concerned, you need to look at the results from those who actually voted.
To use the "majority who did not vote to leave" ignores the fact that (by the same logic) there was an even greater "majority who did not vote to remain".

The "finger in the air test" was seeing the results of elections where the Conservative party were concerned about the votes they were losing to UKIP.

David Cameron announced the referendum, first with a clear statement of the many reasons he believed we should stay part of the EU, but then:
"Three years ago I committed to the British people that I would renegotiate our position in the European Union and hold an in-out referendum.

"Now I am delivering on that commitment.

"You will decide.

"And whatever your decision, I will do my best to deliver it.

From Here

That seems fairly clear-cut. We were given the choice, and David Cameron (presumably speaking for his party) would do his best to deliver on that choice.