I'm going to play devil's advocate here, but I want to preface this by saying I've just spent the last several months absolutely feasting on Kropotkin, Bertrand Russel, Leguin, Chomsky, and Graeber, and generally learning about anarchism as an ideology. I think anarchism is really the only political ideology that actually makes sense of the political and economic upheavals of the last 200 years (rather than say, Capitalism vs Communism, Democracy vs Authority), and it reconciles a lot of issues that people on the right have about people on the left and vise versa.

But one of the issues with anarchism is that it was only popularized as a legitimate political ideology around Bakunin's time -- ~1850s. When proponents like yours and myself and OP (I think Chomsky also described it like this) describe anarchism, it's through the groundwork laid by those who popularized it in the 19th century.

When I learned about things like mutual aid and non-coercive participation, I thought "Wow, anarchism is so misunderstood. It seems the definition has really gotten away from us, similar to the definition of communism," but then I listened to Plato's The Republic and Aristotle's Nicomachean Ethics, and they actually use anarchism with the negative connotation that it still has today! I can't quote verbatim, but they say things like "If X happens, society will fall into anarchy," like it is synonymous with chaos.

So I guess my point is that we have a more fleshed out definition of anarchism due to the thinkers of the 19th century, but the classical idea of anarchism (ie chaos) still persists. In that sense, I don't think the OP really misunderstands it, but hasn't been exposed to what anarchism means as a political ideology outside the classical definition that really is just a synonym for chaos.

Edit: Some of my details are wrong. Anarchism gained traction in Western political thought during the 18th century. Bakunin was an influential figure, but he was preceded by others, such as Proudhon. This is just from reading the wikipedia page. Still, I think its understandable why people still attach anarchism with chaos, because we have philosophers like Socrates and Aristotle (at least in English translations, but then again, the word "anarchism" is derived from Ancient Greek, anyway) using the word in that way.