I'm Irish, I live in NI and I voted to Remain so it's not really my job to advocate for Leave. That said there are a number of things I'd highlight about the vote and people's attitudes to it. I'll leave the larger more existential issues, that I believe lie at the core of the political changes we are witnessing across much of the so-called West right now, aside for the moment.
So...in respect of the vote itself, more complex truths lie behind the simple narratives that have been used to explain the result. Take immigration as an example. A near constant refrain since the referendum is that places where the population is more ethnically diverse, like London, delivered a vote for Remain, and vice versa for Leave, indicating some underlying prejudice in the latter. However, this doesn't provide the full picture. When you look at the statistics for rate of change; the places with higher rates of immigration corresponded with higher Leave votes which points to the problem resting more with the rate of change as opposed to with immigration itself. The following is just a general point about immigration and not directly related to the Brexit debate, but one thing I've noticed is that many people tend to talk about immigration solely in economic terms, as if everyone is some born again Thatcherite whose only interest is money. A person's contentment in society and in their community relies on more than that.
Anyway...the second thing I'd mention is the 'gammon' jibe in respect of the Leave vote. Whilst this may be true to a large extent, once again it doesn't tell the full story as one third of the votes cast from ethnic minority voters were for Leave. I'll have to reread the various analyses published in the wake of the result but I recall that one of the reasons cited from said voters was their problem with the freedom of movement afforded to Europeans, when they felt such preferential treatment should've been afforded to Commonwealth citizens instead.
Some of the above coalesces with the following anecdotal example. A close family friend of ours is a consultant at a hospital in the midlands. He's from Pakistan and has lived and worked in both England and Ireland for around 20 to 25 years now...and he voted to Leave. Shocked and asking why, he said simply - immigration. He explained that he conducts a weekly clinic where he sees around 17 to 19 patients. He said that of that number two thirds are, on average, immigrants. And of this up to half have to be turned away because there aren't enough interpreters available to facilitate the consultation. My father was speaking to him a week or so ago and Brexit came up in the conversation. He has now changed his mind, but the reasons for the vote remain.
So, what are you supposed to say to that? I'm sure the vast majority of people can appreciate that madness of such an experience if it is replicated on any significant scale. To me it just highlighted that there's more to the whole thing than meets the eye.