The sense of having a real say, and possessing actual agency, is very empowering, and very rare, for members of the lower-middle class and the working class today.
The premier strategy for retaining power is to give the powerless a carefully managed illusion of decision-making and autonomy. Having a say over one's life and choices is called agency, and it is the illusion of agency that makes democracy such a powerful tool of control.
The second most effective means of maintaining power is to limit the choices offered the powerless. Offering the powerless false choices, i.e. the choice between two functionally equivalent options, provides the comforting illusion of agency while insuring that the status quo Power Elites remains in charge, regardless of the choice made by the powerless.
For example, give the powerless a choice between Tweedle-Dum (Republicans/Tories) and Tweedle-Dee (Democrats/Labour). Whomever they elect, the self-serving Power Elite of entrenched interests and wealth remains firmly in charge, for the Power Elite speaks with one voice through two mouths, one Establishment Democrat/Labour, the other Establishment Republican/Tory.
If the powerless get restless, make them fearful. This is easily managed via external threats and dramatic predictions of economic doom should the Power Elite be threatened.
If fear has lost its edge due to over-use, then whip up social controversies that divide and conquer the powerless. Divisive, hot-button social controversies are easily staged and media-managed; these serve to distract and fragment the powerless in endless culture wars.
The powerless get very few opportunities to express their dissatisfaction with their gradual impoverishment and powerlessness, and few opportunities to register their disapproval of the Power Elite. They know complaints go nowhere, petitions are ignored, and demonstrations accomplish nothing.
So when a rare chance to stick a thumb in the eye of the Power Elite comes along, they take it. The Brexit vote was just such an opportunity.
Though the benefits that flowed from membership in the European Union may well have been substantial, many people did not have any direct experience of those benefits, which largely flowed to a handful of privileged classes: young, well-educated workers in finance, people who bought housing in London before the huge run-up in valuations, and workers providing services to the wealthy foreigners and highly paid financial professionals.
Many households have seen their quality of life and living standards stagnate or decay during the U.K.'s membership in the E.U. The benefits touted by the Power Elite are either illusory or too modest to matter to these households, and their rage has only grown as the Power Elite tried to browbeat them into approving a membership that yielded no benefits to their households.
The Power Elite simply repeated what has worked well for 60+ years: tout the systemic benefits of E.U. membership, confident in the belief that some of these benefits have trickled down to the lower economic classes, and stoke fears of economic decline if the Powers That Be don't get their way.
Unfortunately for the Power Elite, the benefits of E.U. membership, financialization and globalization have been concentrated at the top of the pyramid: the already wealthy got wealthier, and the young, well-educated, mobile, entrepreneurial class had enhanced opportunities to generate private wealth or at least secure an excellent salary.
A third privileged (i.e. protected) class includes all those benefiting from direct E.U. subsidies.
Those outside these classes saw little if any benefit.
The slow decay of living standards and social mobility was crystallized into anger by the Brexit vote, which was intended to be yet another rigged, illusory choice. The masses were supposed to be persuaded by either the list of goodies that flowed from membership or from fear-mongering about the catastrophic consequences of Brexit.
But neither worked as planned: the benefits were too diffuse or too concentrated in the hands of a few to be persuasive in terms of self-interest, and the fear-mongering only increased awareness of how much the Power Elite wanted a Remain outcome.
Will Brexit hurt the classes that did not directly benefit from E.U. membership? Perhaps. Perhaps it was not in their self-interest to vote for Brexit. But the immeasurable pleasure in depriving the Power Elite of their "democracy" legitimacy was worth any potential sacrifice.
The sense of having a real say, and possessing actual agency, is very empowering, and very rare, for members of the lower-middle class and the working class today. the wealthy and powerful are accustomed to vetoing anything that impairs their wealth or power, and they're accustomed to either winning over or distracting the powerless.
Thus it was a shock when the powerless took the rare opportunity to stick a thumb in the eye of the Power Elite by depriving them of something they wanted.
Is this childish, or self-defeating? Perhaps. But when the system erodes a citizenry's sense of agency, they have little to lose by relishing the chance to use the same power the wealthy constantly wield without any qualm or hesitancy: the power to say "no."