> "the wishes of the people"
The best reason not to proceed with Brexit would be if more than half the people in the country did not want it.
I'm surprised that those who want to reverse the decision don't follow that route.
A tedious election process, a vote denied to 16-17 year olds, floods in London and no doubt many other factors resulted in a 72% turnout and only about 17 million of a UK population of 65.1 million voting for Brexit - with less than 40% of the electorate voting for Brexit and only 2% of those that did vote voting one way rather than the other, resulting in the Brexit outcome.
There is a very real possibility that the majority of the country does not want Brexit and, if I was seeking to reverse the decision, that's the route I'd take.