Be careful in making grand statements like that, using definitions that only a narrow range of people use. Anarchists are not against what most people think about when they think about private property:
To summarise, anarchists are in favour of the kind of property which "cannot be used to exploit another — those kinds of personal possessions which we accumulate from childhood and which become part of our lives." We are opposed to the kind of property "which can be used only to exploit people — land and buildings, instruments of production and distribution, raw materials and manufactured articles, money and capital."
And I find it disingenuous to make peremptory statements about "all anarchists" and "no anarchist". We are a pretty diverse crowd when it comes to the political theory.
Well, that's the entire point of the article, no? To explain what the difference between private and personal property is, and why private property (as defined in the article) is incompatible with anarchism.
And this definition is not some niche one only anarchists have. Basically any political theory has a variation of it, except capitalism, which is at the core about everything being private property.
And this definition is not some niche one only anarchists have. Basically any political theory has a variation of it
And call it differently.
Saying "we are against private property" is understood as "we are coming for your house, for your car, for your kids' toys, for your tools". Proudhon is voluntarily provocative in his maxim but I really think it is counter productive.