I think most people voting in the 2016 referendum were, in their minds, answering the question "do you want to give th establishment a good kicking?".
Doesn’t make sense to me. Seems analogous to getting fed up with shady mechanics, so the next time your car breaks down you drive it over a cliff in the hopes that the wreckage will be more reliable. But I guess people do strange things when they feel like they have no control.
Exactly. Desperate people who don't see anything in the future for them or see thing getting worse, don't usually act rationally. Poverty does that to people as well, for example, and that's visible daily. They resort to payday loans, food they buy might not be healthy for them in the long term and so on.
On the other side there are usually powerful forces willing to take advantage of that irrationality and desperation.
From being an outsider (I have never even visited UK yet), it seems to me from talking to people and reading the news it was more a vote about "do you like how the things are now and where they are headed, or would you like ... something else"? Something else could have been not necessarily Brexit, as long as it was drastic enough change from the status quo.
And I think a good number of people are just dissatisfied and thought this gamble for a drastic change would perhaps improve things.