Edit to clarify: Personal (physical) property rights are considered inherent rights. Outside of any national border, you still own your personal property, because that is a natural right. Governments can enforce property rights, but they don't create them.
The GPL is saying "Here's my work, I'll trade it with you on these terms". The aggression would be in breaking those terms.
Wrong. You do not agree to anything by using GPL software. You must abide by the GPL terms upon redistribution to maintain permission granted by the license.
It is not a contract. The differences between license law and contract law are significant. Groklaw covers the issue thoroughly.[1]
>The GPL is saying "Here's my work, I'll trade it with you on these terms". The aggression would be in breaking those terms.
The GPL does not say that. It says "Here is my work. You may redistribute it under these same terms." It has no requirement you give your changes back to the original author. No trading[2] occurs.
[1] http://www.groklaw.net/article.php?story=20031214210634851
[2] Yes, there is the special case of submitting patches upstream which is by convention, not by license or contractual obligation.
If the GPL is just a contract, then you can now distribute the software as you wish, since you're not bound by such contract. Copyright, on the other hand, doesn't work like that: everyone is bound by default, and you need a license like the GPL to "break free" from copyright's restrictions.