I don't believe that there should be another referendum, but I'm another who voted Remain in 2016, but would actually vote Leave if asked now. Happy to share some of my reasoning.
There's a popular belief that a lot of Leave voters voted Leave for ignorant, ill-informed reasons (e.g. because they're racists or because they lapped up propoganda from the Leave campaign).
However to be honest, my original Remain vote was equally uninformed. I voted Remain because I didn't know much about it all, and I bought into the scare-mongering from the Remain campaign - I suspect the same is true of a lot of Remain voters who remain ardently committed to a Remain position, holding up the concept of the EU as a progressive, Utopian community whilst in reality knowing little about it.
In the past couple of years I've changed my mind, and significantly I have come to appreciate that there is a left-wing argument for leaving the EU, which has unfortunately never really gained coverage, allowing the propogagation of the idea that Leave is a right-wing position and shutting down reasoned debate.
Fundamentally I believe the scope of the EU has grown too far beyond an economic community, it serves big businesses over people, and it represents huge amounts of uneccessary bureaucracy, putting further distance between people and those making decisions about their lives.
Remainers point to the many ways the UK benefits from EU funding as a reason to stay. But the UK are a net contributer to the EU - any funding we get out is ultimately funded by what we pay in. It's massively inefficient to send money into a huge organisation like the EU, on the basis of the benefits that are spat out the other end via EU funding. It also puts further distance between UK taxpayers and decisions as to how that money should be spent. It would be more efficient for the UK to determine how that money is spent domestically.
I'm dismayed at how difficult it is proving to be to exit the EU. When you consider that we originally joined an economic community in pursuit of economic integration, and remained in after a single referendum over 40 years ago, I think it's incredible how the scope and power of the organisation has grown, and how incredibly difficult it's proving to unpick.
Received wisdom at the moment is that EU membership has economic benefits for the UK. But if this position changed, I'm uncomfortable at the degree to which the UK is entwined with the EU. And economists do get things wrong - it was generally thought that we should join the Euro, but it's now widely accepted that we were right not to.
If the benefits of EU membership are such a no-brainer for all member states, I don't understand why the EU is so evidently rattled by the UK's decision to leave?
Freedom of movement gives EU residents (who are predominantly white) preferential treatment in terms of their right to enter the UK over citizens from none-EU countries (e.g. African countries, where the population is predominantly black). In this sense you could argue that FOM is actually inherently racist. It would be fairer to apply the same immigration rules and opportunities to citizens from all countries.
I don't think it's right that the rest of the UK should be held over a barrel because of the Irish border. The population of Northern Ireland is dwarfed by the populations of some urban areas (e.g. the West Midlands and Greater Manchester) - it's not right that NI should be wielding such disproportionate power over this issue.
I'm a reasonable, liberal person and I don't fit the stereotype of a Leave voter at all. But I will vote Leave if we have another referendum.
Lots of people would be shocked in RL to know my position - it's an unfortunate symptom of the toxicity of the whole situation that I don't feel able to be public about my position.