I'm going to look at three aspects of anarchy in the context in which it's being presented on social media: what it is, what it does, and what we can do with it.
What it is
Anarchy in the sense I'm describing it here is "statelessness." Anarchy in various forms (including Communism) has always been a force in politics; ignore it at your peril. It's also a useful safety valve and political thermometer; anarchism tends to take root where social problems exist as the solutions presented seem more attractive the more desperate and disenfranchised the people are. Therefore, while I'm no fan of anarchy as such I tend to keep an eye on anarchist movements and even have some sympathy for some of their positions, particularly those that are beneficial to the community in general, e.g. Occupy's debt forgiveness scheme. I don't hate anarchists but I disagree with them on the idea that it can scale to a national level. History says, "No it can't."
Multiform and ever-evolving
Anarchy comes in many forms and with many names, mostly because people appear to be uncomfortable with anarchy's other meaning, "Lawless disorder." Anarchists aren't necessarily disorderly as such, they just don't like the idea of being subject to an hierarchical authority, e.g. the state. They can be either individualist or collectivist or a mix of the two (either extreme can be a lot of fun to play with. These are the people I troll). The one defining thing they all share in common is a visceral hatred of the Establishment, which they tend to refer to as "government" or "the state." Their ideological narrow-mindedness can be pretty unnerving to behold.
What it does
The idea of the decentralised stateless society in which there are no taxes and people interact via purely voluntary transactions is never going to go away as long as some clever clogs can find an intellectually challenging way to present the idea as rational and plausible; Pirate Party founder Rick Falkvinge, who has now publicly espoused an anarcho-capitalist worldview, has been discussing them lately. I had a bit of a giggle pointing out the fallacies in his rather facile arguments: the world and its political systems can't be as neatly explained as he presents them. If they could, private cities might actually work as a microcosm of voluntaryism that eventually causes the state to wither away. Hah! No such chance. The emergence of state capitalism following the implementation of the Soviet system is proof that human nature won't allow it. Anarchism may work on a small local scale but when it comes to providing infrastructure and services on a large scale, even in emergencies, it epically fails because individuals and groups don't or won't cooperate or get with the program unless it suits them.
Some historical examples
Two examples of anarchy failing to achieve much beyond a local level that spring to mind are the Paris Commune and the Articles of Confederation. Short version: when any system is entirely voluntary the people involved in it have the right to refuse to cooperate. Lack of hierarchy means lack of leadership. You can't run a company like that; when individuals and groups fail to communicate and share data and resources effectively the department becomes dysfunctional. This is what pulled the Paris Commune and the early Confederation apart, yet anarchists like to imagine that their iteration would succeed where other movements failed because they're better thought out and if people would just get with the program... there's your problem.
It requires blind idealism
Anarchists either can't or won't accept that disorder and disorganisation is inherent in a completely decentralised system. Whether they are left or right-leaning they insist that they could make it work despite the mountain of contradictory evidence.
#UBI pie in the sky: how giving people free money makes them better off for as long as they keep receiving it. https://t.co/ONJAgIKof4— Wendy Cockcroft (@wendycockcroft) September 5, 2016
Universal Basic Income is a sacred cow for many anarchists (and idealists) as they believe in its powers of Star Trek-ability, innovation-generating, and abusive spouse escaping, etc. I actually got into a scrap with Mike Masnick on Techdirt about it on one memorable occasion because I'm pragmatic by nature and couldn't see how the maths added up. "Don't worry your pretty little head about it" isn't a convincing argument and I have yet to see one made. I look forward with undisguised glee to seeing the Finnish experiment, erm, finish. And I predict it'll go out with more of a whimper than a bang, way over budget and failing to make long-term tangible improvements in its subjects' economic lives like Dauphin in Canada and the Alaskan debacle, which turned out to be dwindling dividends from the state's oil revenues. Like, I didn't see that coming!
Remember my post, "Come The Revolution: Good Luck With That!"? It seems that some people are staging them all by themselves, with predictable results. The Sovereign Citizen movement and its offshoots denies the authority of the state. That people are rebelling against the Establishments in their respective nations is the Establishments' own fault for failing to give people a stake in the state. The disenfranchised and the disenchanted don't always take it lying down. That they end up funding and supporting alt-right loons to remedy their situation is a symptom of the problem, not the cause; Phyllis Schlafly would have got nowhere if the socio-economic conditions of the time hadn't handed her an army of home-makers ready to rally at a moment's notice. And make no mistake, she was a revolutionary — and, at heart, an anarchist of sorts, though you might not have got her to admit it.
When noisy pressure groups attract sufficient numbers of activists, expect change. The Tea Party movement has resulted in a plethora of offshoots, one of which is the emergence of the alt-right. Since alt-right voters tend to vote in alt-right candidates the results should not surprise us. Given that their stated aim is to "shrink the state to the size where we can drown it in the bathtub," government shutdowns, politically-motivated obstructionism and failures to deliver actual governance should not surprise us. If an anarchist is voted into office and attempts to demolish government by obstructing governance, that's the idea.
Anarchy fails on a large scale because governance demands leadership and leadership requires systems of information processing and sharing to enable efficient decision-making. This is, in and of itself, antithetical to anarchy.
It's why they love to rail against bureaucracy; information storage, processing, and sharing can be used to hold individuals and groups accountable and enable control of them. However, bureaucracy in and of itself is not a problem if it is efficient. It's when it's run for its own sake that it becomes problematic.
What we can do with it
Given my rather scathing indictment of anarchy you'd think I had no time for it at all, except as a fringe philosophy that occasionally moves its adherents to do good deeds or as a way of taking the public temperature. Actually, there is more to anarchy than that and we can actually harness it for the good of the community if we pick out what's best about it and leave out the parts we don't like.
The most staunch allies activists tend to have when campaigning are anarchists. During the ACTA fight it was the anarchists who kept sharing anti-ACTA posts and who argued in favour of pushing back against it. They got the ball rolling and kept the momentum going. It is the anarchists who lead the fight against unfair FTAs and sneaky treaties, asking awkward questions and staging protests to raise awareness.
Social justice used to be about balancing the scales to give everyone a reasonable chance of achieving success in careers, etc. These days the term has been hijacked by left-liberal class warriors and political protectionists to advance a culture of outrage that demands a torch-and-pitchfork-bearing mob's attendance at once at whatever they feel is aggrieving them today. Ignore that, I'm talking about good old-fashioned fairness; anarchists can help us with that via activism and by setting up projects that either raise awareness or actually solve problems, e.g Streets Kitchen.
Anarchists are a necessary part of our political fabric because they're at the edges, testing the limits of freedom and of the boundaries between the freedom of the individual to act and the will of the people being respected. They stimulate and encourage debate and I'm in favour of anything that makes me think.
Anarchy doesn't scale. On some levels that doesn't matter as it doesn't need to scale, it just needs to stay at the fringes where it belongs, testing the limits of our moral and social standards. It's when those in power abdicate their responsibilities in favour of a quasi-anarchist "neoliberal plus" society that I have a problem with it. Let the idealists dream, I say, but for the love of God don't put them in charge.