Proponents of the GPL don't see it that way. Rather than seeing it as the creator's right to choose the terms, they see it as the consumer's right to access and modify source code.
That's the fundamental split: copyright normally gives the creator the "right" to take away the consumer's rights; the GPL merely prevents this and maintains the consumer's rights.
As others have pointed out, the idea behind copyright is to give a creator a limited monopoly over some information (ideally in order to encourage arts and science). The GPL subverts this: not only does the initial creator give up the monopoly, but the license ensures that nobody can subsequently reclaim a monopoly on the work in question. That is, the GPL involves not only giving rights to your consumers but also making sure as many people as possible cannot take those rights away again.
Essentially, it shouldn't be the creator's choice at all. The consumer has some rights (like being able to see and modify what runs on their computer) and these rights should not be infringed. That's entire core of the GPL and that's why it's the opposite of copyright normally: it protects the consumer and not the producer. The fact that it happens to be implemented on top of copyright law really is an implementation detail--if it was possible to pass a law protecting the right of every computer owner to be able to access and modify any code running on their system, the FSF would surely support it.
In summary: the GPL is about the consumer where copyright is normally about the producer. That's why they are different.
That's the fundamental split: copyright normally gives the creator the "right" to take away the consumer's rights; the GPL merely prevents this and maintains the consumer's rights.
As others have pointed out, the idea behind copyright is to give a creator a limited monopoly over some information (ideally in order to encourage arts and science). The GPL subverts this: not only does the initial creator give up the monopoly, but the license ensures that nobody can subsequently reclaim a monopoly on the work in question. That is, the GPL involves not only giving rights to your consumers but also making sure as many people as possible cannot take those rights away again.
Essentially, it shouldn't be the creator's choice at all. The consumer has some rights (like being able to see and modify what runs on their computer) and these rights should not be infringed. That's entire core of the GPL and that's why it's the opposite of copyright normally: it protects the consumer and not the producer. The fact that it happens to be implemented on top of copyright law really is an implementation detail--if it was possible to pass a law protecting the right of every computer owner to be able to access and modify any code running on their system, the FSF would surely support it.
In summary: the GPL is about the consumer where copyright is normally about the producer. That's why they are different.