Why GAN is Unsupervised Learning?

While teaching the Generative Adversarial Networks (GANs) topic in the ML/AI class, a question I often encounter is, "If we have a feedback/supervised learning [for Discriminator], then how come is GAN [totally] Unsupervised [model]?"
For example, we have a clustering algorithm or PCA, etc., which doesn’t take any feedback from the given data and mines it automatically; GANs are a bit different in their supervised learning (even if it’s for Discriminator only).

So should we call them Semi-supervised, or what?