Today it may be something that makes you happy but one Day you will vote for something and you will realise too late... your vote is worthless.
If one believes that public referendums give meaningful results (which is a whole other question - there's a reason we've largely moved away from direct democracy), then what's the harm in having another one to check the result?
Leave votes, for whatever reason, cast their vote based on the information available to them at the time. I'm not going to judge anyone here, or imply that anyone voted wrongly. I'm just saying that the vote was made in the light of incomplete information.
Now, 2.5 years later, we have more information about what a Brexit deal would actually look like. Where's the harm in seeing if that's still something people want? Why should we pick one specific vote, at one moment in time, and cast it as sacrosanct? I mean, heck, the PM has made parliament vote on her deal twice already, and is gearing up for a third go round. Is that democratic?