It was supposed to be a suggestion, not a mandate, because it was an “advisory referendum.”
It’s more complicated than that but it certainly isn’t as clear as we told you what to do, now do it.
Even Nigel Farage agreed it was advisory (from the cite above):
This might be the only time I’ve ever agreed with him. It would be too complicated to explain to everyone whether a referendum was advisory or binding, and people have the impression that they’re binding, so it would be better to make them binding from now on, and oblige the campaigns on either side to comply by really strict rules, because it’s binding and a big deal.
But the rules under which the Brexit referendum was conducted were advisory and very vague. It went ahead pretty quickly and there was still debate about what age to allow people to vote, because there’d been a referendum in Scotland not long before, and the age there was 16.
We don’t have a lot of referendums on the UK and almost all of them in the past 40 years have been related to devolution: https://www.parliament.uk/get-involved/elections/referendums-held-in-the-uk/ I’m 43 and had one opportunity to vote in a referendum before the Brexit referendum. For most people in the UK, they’ll have voted in one or possibly two since the original EU referendum in 1975, they were old enough then, and if you live in England outside London you won’t have voted in any other referendums since then.
They’re not a common occurrence and the rules are different for almost all of them.
But the way it was phrased, it seemed like a mandate, which is why people are assuming it was. So Brexiters will feel rightly cheated if their choice is taken away from them even though, technically, they were only meant to try to advise MPs in the first place. Those voters were wrong on a technicality but it’s really quite an obscure technicality that it’s unreasonable to expect most people to know.
And most of the areas that voted most strongly in favour of Brexit lived in areas where the only referendum they’ve ever heard about prior to Brexit (a change to the first past the post system, put forward by the LibDems in 2011 as part of their coalition deal with the Tories) got bundled up in a lot of other stuff and was largely ignored.
TLDR: It was advisory, but there are reasons that many voters didn’t realise that.