"Anarchist" is pejorative in most countries, but in Italy Anarchism has a rather positive aura -- intellectually, but not in practice. That's because the Anarchists were much involved in the political movements that led to the expulsion of foreign colonial governors (from Spain, France, and Austria) and the independence and unification of the country. They played the role of the American activists who first spoke and conspired against the rule of Britain, I guess. But, of course, as soon as the country was unified, the Anarchists were thanked and pushed aside, and monarchy was established (with a branch of the French House of Savoy on the throne).
Mussolini and Hitler also indirectly benefited from anarchists who called on people to refuse to take part in the "political game" of "sham democracy", and thus helped weaken the governments that they then took over.
You don't get to redefine terms to fit what you believe. Proudhon invented the term, so he can define it any damn way he wants - even if that means a social order that he desired, but you don't believe can exist.
Unlike Proudhon, I am neither a socialist, nor an anarchist, so I won't try to make his argument for him - but I am at least well-read enough to know what the term means, and to use it as it was meant to be used. If you want to discuss 'chaotic lack of order', then you should use that phrase, or maybe make up one of your own - but using the term 'anarchy' is just incorrect.