Politicians will want you to believe Brexit is a big bad deal because they lost face. Brexit is a great big deal for the people, towards self-governed freedom and sovereignty, with all the uncertainty that comes with such freedom.
Britain was in a bad relationship. With a partner abusing its position as a growing undemocratic society, laying down its arcane rulings on unsuspecting Brits, and getting paid handsomely for doing nothing but rule.
People should be happy about the breakup because any breakup is useful to reset the bounds of freedom for humanity and perpetuate the right to a pluralism of freedom. It is only scary for those who are more comfortable latching on to the bosom of stifling socialism, as the Stockholm syndrome from a totalitarian regime of freedom in Europe.