I think — as a Remainer who remained so hard I responded by moving to Berlin — that "why" is "because it was a referendum and that's how those work".

It's not sufficient (or necessary) to be correct to win in a democracy, winning requires being convincing, which may be easier with the truth but is also much harder when insulting half the electorate.

Even when it's very tempting afterwards to say "we told you so".

As for how to be convincing… dunno. I'm much more comfortable with computers where I can google the errors.