Gradualism is the idea of preferring a "gradual, as opposed to an immediate and rapid" approach to abolition (freedom from State coercion). Rothbard advocated against gradualism and instead asked the libertarian to support abolition as soon as realistically possible. Actually, his discussion comparing and contrasting the two positions are a bit incoherent; or, at least for me, difficult to understand because realistic abolition could, at times, be gradualism in practice.
Of course, the magical button does not exist (and most likely could never exist). But it does bring up a good question for the critical thinker. Recently, Jeffrey Tucker wrote an article about the same topic, where Tucker concluded that he would push the button. After all, "[t]he state makes no existing productive contribution to society that couldn't be immediately replaced by private provision." For the libertarian (especially the anarchist leaning one) this is completely understandable (though I may critique his use of the word "immediately"). Indeed, it's why one is an anarchist in the first place. And I think the current total of 68 CTIR Episode podcasts prove this argument (though maybe from a minarchist position). However, Tucker misses an important point.
Before we get to that important point, let's focus on Stefan Molyneux's answer to the same question. According to Tucker, Molyneux concluded that he would not push the button, likely because "he didn't think we as a culture and people are prepared for instant, unexpected freedom."
NOTE: If you did not already know, both Tucker and Molyneux are current "leaders" or "great minds" in the "libertarian movement." (It sucks to think critically, having to use air quotes all the time).
What's interesting about both Tucker's and Molyneux's answers are that they both miss a crucial point: that they - individually - choose to press (or not press) the magical button. This blows my mind! Who gave either of these two individuals (or Rothbard for that matter) the "natural right" to push (or not push) a button that could change life forever (whether for better or worse). Indeed, the very act of pressing the button seems to be an act of aggression, to which I - nor anyone else - has specifically consented to.
One could argue self-defense, but that must also be both reasonable and, at minimum, proportional to the initial aggression. Is it reasonable to push a magical button that could cause massive changes in our daily lives? Of course, I'm not arguing that massive looting or rioting would occur, but the people who are prepared (especially the agorists in the libertarian movement) will have a much easier time living the consequences (imagine all the "gun control" supporters instantly flocking to purchase firearms). Moreover, is the end of the State proportional to its invasion of our individual property rights? I suppose it depends; if I have yet to serve time in jail or be fined for anything, I have a weaker argument. Similarly, if I have received more in benefits from government than what it has stolen from me in taxes, it seems I also may have a weaker argument (unless, of course, you are an individual who believes it is proportional to murder a state employee simply because of their occupation. But, to be fair, we all live with a great deal of additional negative consequences beyond taxes as a result of government intervention (i.e. inflation, unemployment, debt, etc.).
The analysis is even worse if one applies the idea that individuals have a natural right to use self-defense to protect others. What if the "others" don't want you to push the button? What if they enjoy the State? What if they define "freedom" as living under the State's care, provided with welfare and employment? What if they support the gradualism approach instead? What if they wanted to have the choice of pushing the button?
More importantly, what if the button did not in fact end the State? What if it instead led to the cloning and breeding of millions of the two "stars" below?
Well, Mr. Smarty Pants, what would you do? Shoot. I wouldn't want to be anywhere near that magical button. I don't even want it in my peripheral vision. Just lock it in a box and drop it in next to the bodies of Dexter's victims. I don't want - nor did I ask - for this responsibility. Indeed, I don't even have the right to make such a decision. I have consent from nobody - whether explicit or implied (not even my two children). Nor would I ever want such responsibility.
And I thought that's what libertarians and anarchists alike wanted: for each individual to decide for himself or herself. Even the great Rothbard seemed to agree: the most fundamental and natural right is self-ownership; basically, the right to do whatever one wants as long as it does not invade the property rights of another. It's the basic axiom to libertarianism! Yet we also would happily and quickly push a magic button that would end the State and thus effect the lives of billions worldwide? Something about that just doesn't seem right. I would never want such responsibility - if I did, heck, I'd probably run for President or something.