To give you a less conspiratorial answer than other, because those that stood against it were labelled as being against "the will of the people". Basically even though it was non-binding, those that were pro-brexit clothed themselves as following democracy, and those who opposed them as anti-democratic.
There were several problems with the referendum:
-
It was called to try to quell a split within the conservative party. Not because of any real movement in the country.
-
It never specified what "leaving the EU" meant. When, how fast, what remaining relationship? So the debate was nebulous. Positives were extremely optimistic and negatives were dismissed as pessimistic (despite being true).
-
The non-binding nature meant that no margin of certainty was set. It should have needed a majority of the voting public, or > ⅔ to be taken as something we really wanted to do. It was too major a change to enact on 52-48.
-
We don't govern by referenda in the UK. They go against the principle that parliament is sovereign because they place the people's voice above parliament's. We're a representative democracy and not a direct one. The only other ones we've had are
- 2011: The Alternative Vote voting system held a few year before. Also called by David Cameron and also a complete sham of a process.
- 1975: Continued membership of the European Community. Called by Edward Heath to quell the same split in the conservative party.
Hence the rules that surround referenda are poorly specified.
Top choice of phrasing there BBC.