Let's start with a few unpalatable truths. Anarchy - understood as a society that rejects power, where all associations are voluntary - is never going to happen. Neither, for that matter, will communism, or unrestricted free-market capitalism. The human race as we know it is probably not going to survive for much longer, either: there are too many outside forces that can kill us and ways that we have devised to kill ourselves. Even if somehow, in the limited time we have left, we were able to isolate all the anarchists on the planet and let them form a society, we would still not arrive at anarchy. For one, our cultural biases (mostly statist, patriarchal, power-loving, violent) are too strong to let us arrive at a peaceful arrangement. Secondly, very few anarchists today are in agreement. In the absence of a realistic political goal to move towards - or even the possibility of such - we've taken refuge in theory, becoming 'hyphenated anarchists'. So what's the point of being an anarchist?
You might say that anarchism is right inasmuch as any political philosophy is right. It diagnoses the problem with society as concentrations of power, primarily state power, and you might think this is more accurate than the communist view that the problem is with the way money works. You might even think they amount to much the same thing! But all this thinking and thinking is sterile: it provides no course of action other than revolution, which is both bloody and futile. Can anarchism guide our actions in a more useful way?
I think it can. As a Stoic, I dismiss out of hand any wish to involve myself in the realm of large-scale politics - voting, for instance, joining a revolution (to some extent, even protesting) - because large-scale politics is totally out of my control. I dismiss out of hand any wish to prevent further concentrations of state power or exercises of state violence - sabotage or raising public awareness, for instance - because to prevent this is totally out of my control. What's left, after these two wishes are dismissed? Only anarchy as it pertains to daily life.
When IOZ and Jack Crow claim that anarchism entails radical feminism, they're arguing for the practicality of anarchism. Being aware of and repudiating rape culture, trying to avoid situations where women justifiably feel threatened, listening to what women have to say - these are useful things that all anarchists should do, since they minimize the amount of coercion one exerts on others. Joining rallies and vandalizing government buildings are secondary, since they have far less positive effect. So practicing feminism is one useful way to practice day-to-day anarchism.
There are other things we can do as well. We can treat those with less power than us in ways that don't rely upon the difference in power. We can think hard about using insults that are insignificant for us but significant for other people, insults that usually highlight their lack of power. Does this sound familiar? It should: it's pretty much the idea that we should be aware of our own privilege, or the myriad of power structures that we're embedded in at birth. Health, ethnicity, wealth, gender, sexual orientation, nationality - all these things let us coerce others in socially acceptable ways that are invisible not just to those around us but to ourselves. If we anarchists are committed to rejecting coercion - rather than just rejecting state coercion - then we need to regularly check our privilege.
This is something like Charles Dickens' idea of revolution: not a revolution put in place by force, but a revolution inside the heart of every individual. In short, anarchists might not be able to create a decent world, but - if our politics is valuable in any way - we should be able to make ourselves into decent human beings.
Thanks to Prof Crispy for his definition of anarchy as a society where all human interactions are entirely voluntary. Thanks to Jack Crow for, somewhere in the comments chez IOZ, saying that 'his anarchism was not hyphenated'. I've used both of these in my post.
This, if anything, is the anarchism I believe in - this is the core of my political philosophy. In other words, my personal anarchism entails my political anarchism, not the other way around.