Are coperatives the ultimate redpill?

I see what you mean but I never quite understood why people here consider coops to still be private property. I mean, yes in the traditional sense of the word they are private property but when we analyze what they are can we really say they are? Why can't we just say they are collective property? Even if it isn't state/public property it still is of the workers, owned by them and worker by them. They aren't private property. Also what do you mean by "fully socialized"?

What they are is private property, as in property owned by a group of private individuals for their own economic benefit rather than being owned by society as a whole.
Owned collectively by society as a whole, not just collectively by a handful of people.

Why should the entiriety of society own and benefit from them if only said workers of that business work there and manage it?