The irony of "public property"

I recently had a conversation online with a socialist retard who seemed to think (like so many socialists do) that complete governmentless anarcho-capitalism is the only possible form and definition of "capitalism", and anything that deviates even slightly from that is "not capitalism" (and, obviously, a form of "socialism", because apparently in their view there exist only two economic systems in this world: anarcho-capitalism and socialism, and if something doesn't fit in (their definition of) the former it has to belong to the latter).

(Of course in reality there are more forms of capitalism than just complete anarcho-capitalism, such as laissez-faire, and welfare capitalism, for example.)

Anyway, during that conversation the concept of "public property" came up, and I realized an interesting irony about that concept.

In general, anything owned by the government is "public property". This is in contrast to "private property", which is owned by either an individual citizen, or a company.

But what's this "irony" of that concept of "public property"?

"Public property" is in principle owned by everybody, but quite ironically nobody owns public property. It sounds like a complete contradiction of terms, which is were the big irony resides in: Public property is owned by everybody, but you don't own any public property.

If you own something, that something is by definition "private property", because it's under your ownership. Thus, if something is "public property" then you don't own it. It's the "property of the people", and while you are a member of "the people" you do not personally own it (at least legally speaking).

Because you don't own it that means you can't do whatever you want with it. It's not yours to do whatever you want. You can't just take it for yourself without permission, and you can't damage it. In fact, if you damage it you'll usually have to pay for it, or face jailtime (which is a very clear sign that it's not your property and you can't do whatever you want with it). The only thing, usually, that you can do with public property is to use it. For example most sidewalks and roads are public property, and you are entitled to use them (but you can't eg. vandalize them or remove them).

Thus, whenever someone (eg. a First-Amendment auditor) says "this is my property" (when talking about public property) he is incorrect. He does not own that property. It's public property, not his property. It belongs to everybody, not him (even though he is part of "everybody"). Which is the big irony.

If you want to assign an "owner" to public property, it would be the government (although perhaps it would be more accurate to say that the government "controls" public property rather than "owns" it. In a sense the government cannot own anything, because anything that it "owns" is property of the people. Of course the nuances of law regarding this varies by jurisdiction.)