It's the belief that economic freedom, à la deregulation and massive tax cuts, especially for the wealthy, will lead to greater political freedom.
Not only has that not happened, but it also has, in some places, led to greater political corruption, oligarchies, and more money for rent-seeking on a scale commensurate with increases in wealth at the top end of the economic heap. So it turns out that economic freedom isn't as fungible as many people believed.
Other factors such as the local sequelae of globalization, immigration, and the rapid pace of social change may be behind the rise of authoritarian attitudes, but it's pretty clear that neoliberalism is not the antidote. Moreover, it may exacerbate rising tendencies toward authoritarianism as those who are stagnating look to strongmen to save them from their purported enemies.
This is also a view I espoused in my more Libertarian and Republican incarnations. One reason I believed in this idea was that I thought economic freedom would give people a taste for freedom more generally. I also bought into a reductionist-logical mindset that saw economic and political freedom as rooted in the same principle of individual liberty. Show people one kind of freedom, and they'll understand and accept the other because they've implicitly accepted the underlying belief. As a philosophical exercise, that sounded compelling to someone who was naive about how the mind works. In some sense, it was a Randian way of looking at human behavior. Of course, people don't think that way. People have many more emotional factors involved, biases, group identifications and interests that give rise to beliefs that are often contradictory. A logical argument isn't compelling in the face of such beliefs, and even when the logic is understood, simple pragmatism often overcomes the logical argument.