I think that it's largely to do with the basic misconceptions that people believe in. Some people are stupid, some are ignorant and some are misinformed. I have no doubt there are good reasons to support the 'No' vote. But how many people who voted for it did so with clarity of judgement is likely to be depressingly low.
A big part of the 'No' campaign was based on misrepresentations, and outright lies. For example, the 'more coalitions' argument was peddled by many a campaigner, despite a total lack of evidence (and in fact evidence to the contrary) to support this claim. Another example is on the quite frankly unbelievable assumption that running the referendum (which was always going to happen anyway) and using the system in the future was costing servicemen's lives. The list of similar atrocities to the quality of British politics goes on, and some of which people believed. This includes 'it's fairer' (which, upon investigation, is a statement of loose interpretation), 'it means the BNP will run the country', 'it destabilises government' and the personal attacks on people backing the 'Yes' vote - to name a few.
It doesn't help though, that AV is really only an overcomplicated compromise between FPTP and PR. Really, everyone wants PR (Proportional Representation), and why we didn't just vote for that will probably be the subject of great debate among the Lib Dem elite, and frustration amongst everyone else.
The 'Yes' campaign was, quite frankly, not good enough. They were hardly anywhere to be seen, and they managed to throw away a massive lead in the polls to what now appears to be a crushing defeat. Most of the people I knew personally were voting 'no'. When I asked them why, it was almost always was because they either backed the 'No' campaign (which, as mentioned, rested on many a falsehood), simply didn't understand AV (and thought it was all too complicated), or a combination of those two things.
Ah well, what can you do, eh?