Non binding would be the key phrase you're missing with that.
The UK isn't a direct democracy, and the vote wasn't legally binding.
Your mixing up it not being political viable with any legal democratic process, hope that clarifies it for you.
It's also stunningly ironic that you are echoing the leave argument of 'you lost so shut up', not only does that fly in the face of the concept of free speech and political discourse, but requires people to forget that leave has done exactly that since the 1970s!
Oh and edit to add, Leave's own poster boy said before the outcome was know that a 52/48 split would leave the result unresolved and maybe need a second vote.
https://www.bbc.co.uk/news/amp/uk-politics-eu-referendum-36306681