This is what Socialists don’t want to believe. When everybody owns something, nobody owns it and nobody cares.
I get what you are attempting to say, but it really makes no sense because it can't be both. One either owns something or they don't. Also, human nature pretty much guarantees folks will always care if they think they have less than someone else and when they have more than others, they will do whatever they can to hang on to it. 'Survival of the fittest' comes to mind.