Question About Discriminator of CycleGan
This is explained in the original CycleGAN paper:

For the discriminator networks we use 70 × 70 PatchGANs, which aim to classify whether 70 × 70 overlapping image patches are real or fake. Such a patch-level discriminator architecture has fewer parameters than a full-image discriminator and can work on arbitrarily sized images in a fully convolutional fashion.

Therefore, the arguments for using patch-based discriminators are that:

It has fewer parameters.
It enables using them in arbitrarily sized images.