What is nature?
For Garfield, nature is an illusion. The cat perpetually flaunts established rules of propriety. He is a "bad cat" who, by refusing to play along with the normative cultural and social expectations imposed on his kind, effectively "queers" established binaries of natural and unnatural behavior throughout the animal kingdom.
It is accepted that cats will hunt mice in order to kill and devour them - this is the behavior we associate with felines of all species. Cats are hunters, according to the stereotype, whose instincts have not been dulled by thousands of years of domestication. Garfield, on the other hand, rejects the tyranny of "instinctive" behavior: he refuses to play down to expectations placed on him by convention and propriety.
Examine his posture in this strip: he sits up on his haunches (how like man he is!), placidly leaning over an ottoman, unwilling to express so much as a flicker of interest in the prospect of hunting and killing the cat's supposed natural prey, the common mouse. He dispassionately observes the mouse, responding only to the voice of his supposed "master" and "owner" who upbraids him for failing to fulfill his "duty" of ridding the master's house of vermin. His disapproval at Jon's voice is manifest in the second panel. (We might assume from context that it is Jon, even if we are given precious little corroboration of this fact - what if the voice is not Jon, what if the voice instead of Garfield's internal conscience, constantly admonishing the cat to resume his "natural" role as a cis-feline?) It is only in the third panel that we are finally allowed to see Garfield smile: he has successfully stymied the presumption of programmed biological "destiny" that undergirds the extant master / slave relationship between owner and pet. It is not in his interest to hunt mice because he has made the rational decision to reject his servitude in absolute terms.