I don't have to make my work publicly available. I could make it hidden forever or for long time, or to closely share it with a limited number of people.
I can compose a music piece, paint an art, or write a book, and never tell anyone about it. I can do it just out of a pure creativity interest, and without the need to make anything in exchange from the public.
In this case my creativity would be a property in it's very ultimate sense.
I believe that in it's very root the Copyright laws were established to offer something to creative people who truly don't need to be a part of the society, who make their creativity for themself out of a pure genius without the need to receive any reward for their labour. In exchange that they make their work available to public too, so the entire society would benefit from their creations.
This is the offer of the government that grants the author a personal monopoly to their creativity, but this creativity is a Property before it was published.
We can erase this offer, saying that one's work is not truly a property. Well, we can do so, but we can't enforce an author to give up of his property and make it publicly accessed whether we consider it a property or not.