There's an old joke in which a man asks a woman if she'd sleep with him for a million dollars. After some thought, she says yes. Then he asks her if she'd sleep with him for 50 dollars. She says, "of course not! What kind of girl do you think I am?"
"We've established what kind of girl you are," he replies. "Now we're just haggling over the price."
When it comes to a lot of the more vocal proponents of abolishing copyright, that punch line applies.
The problem with a large part of the anti-copyright crowd is that they don't understand or won't admit what copyright entails as a concept. That is the right of the creator of a work to exert some control over how it's used, who can copy and distribute it, and a right to have their authorship acknowledged.
These members of the anti-copyright crowd cite the GPL (GNU Public License) as an alternative to copyright without any sense of the ironic fact that the GPL can't exist without copyright. They're proposing a solution while simultaneously advocating the destruction of the thing that makes their solution workable. While the GPL is less restrictive than other licensing methods, it's a license and it does impose some restrictions on or conditions for use of the work. It is a method of controlling your work. But without copyright, the GPL could not be enforced.
Without copyright, the creator would have no power to dictate any licensing terms, even the GPL's licensing terms. Their work would go into the public domain and anyone anywhere could use it in any way they wanted. Drop the argument of whether or not profit motive drives creation sufficiently enough that it needs to be retained. Let's look at what happens if the GPL is unenforceable.
You create some cool open source app. Then some megacorporation comes along, removes all your claims of credit, adds 10% more code, compiles it, and distributes the executable binary locked up in DRM. Under the GPL, you could retain your own lawyer or appeal to the FSF to sue them and force them to open up their application. But without copyright enabling you to dictate licensing terms such as the GPL, you have no legal recourse. They get away with it and the worst they suffer is some bad publicity... maybe.
Would that theft of your work act as a disincentive to creating more works? Would you say to yourself, "why bother slaving away to create this when some megacorporation can just steal it, put their name on it, and lock it up in DRM"? Perhaps you would. Perhaps you wouldn't. But some people would and that would take more creators out of the market and lower the quantity and quality of content that's available.
Those who hold up the GPL, Creative Commons, or any licensing option other than the public domain as an alternative to copyright are expressing a preference for allowing creators to exert some control, however small, over how their work is used and distributed. But if you abolish copyright, you take away even that small element of control.
Now we can argue until we're blue in the face over the details of what copyright should allow and should not. The extension of copyright terms, the constant chipping away at the doctrine of Fair Use, the evils of DRM... these can all be cited as things that are wrong with current copyright law and things that need to be abolished. But that's reforming copyright, not abolishing it. It's surgery on the patient, not euthanasia.
If you support the GPL, support an author's right to dictate any terms regarding how their work is used, then you support the concept of copyright even if you don't support the current law and practice of copyright. Then the argument becomes not whether copyright should be abolished, but what form it should take. In short, we've established what kind of girl you are. Now we're just haggling over the price.