I have been debating these topics for a long time and I am pretty sure that it all boils down to that distinction. The libertarians are right that the state creates monopolies, and that most of the problems we face are the product of government, and that the government exacerbates those problems. The left is right in that the market works slowly and that there are consequences to relying upon it exclusively. Some people seek to define the best balance of market and state. Others seek the extremes.
I am not sure that there is anything magical. I think that libertarians prefer to pay one set of consequences, and statists to pay different consequences. A libertarian is perfectly OK with it taking ten years to solve a problem. A statist isn’t. A libertarian would rather have to battle an irresponsible corporation using the market than an irresponsible government that is outside the market. And in the end, that’s really the only difference.