the best explanation I heard from a leaver...was that he was very patriotic and he felt we should control our borders and make our own laws, he didnt necessarily want to see a fall in immigration, he just wanted us to control it. There were not specefic laws he wanted to see changed, but he knew he wanted us to make them. Now Im not patriotic at all, I think it possibly/probably does more harm than good, but to this guy it meant a hell of a lot and to him it was important that the laws that effect where made by us.
Another who worked in my field (conservation) had tried for years to influence and change CAP, he felt it would never been changed for the good, so felt leaving was the only way to see change there...so far the signals look like he may have been right?
The second point was very specific, a single issue decision for him, the first was something quite intangible, I disagree with both of them....but can also understand and respect their vote.
...whereas before that I might have just dismissed someone as a short-sighted, blinkered idiot who just blindly went along with something without being able to debate or explain why they thought that way instead I started accepting people's views, I wasn't dismissive, I didn't do any name-calling, I simply asked such people to explain their reasoning to me to try to understand why they thought that way...I did that for at least 2 years after that video, mainly inviting Leave voters to discuss things with me. My conclusion from that exercise was that all but literally TWO of them were short-sighted, blinkered idiots who just blindly went along with something without being able to debate or explain why they thought that way.
Of the two people who accepted my invitation to explain their reasons, one of them had done it as a "protest vote" as he "thought it was worth discussing" but was horrified that Leave had actually prevailed and would never have voted for it if he'd thought that would be the outcome - he also thought (and still thinks) that the government made a complete mess of it.
The other freely admitted that his was a completely selfish position based on his own job and the fact he has no children nor any plans to have any. He accepted that there were lots of lies told that he had believed but he still stuck by his vote, however, was still not happy with the way the Government handled it and is dreading a no-deal Brexit.
So the short version is that you can't have a reasoned debate with someone who doesn't want to debate and who can't explain their reasoning. I will concede that a lot of that reticence was clearly due to past experiences (e.g. an initial response of "Oh you'll just call me a racist!") but even when I gave every reassurance that I had no interest in name-calling or labelling and just wanted a calm debate, that was the outcome - just 2 people out of literally hundreds of people in that time period were OK to discuss their reasoning.
So, it's easier said than done.