Beneath every close friendship runs a terrifying undercurrent of hatred. You know each others' pressure points, anxieties, and secrets. The tension is in the knowledge that these powers could be unleashed, the pact is that they will not, the reality is that they seep out in small doses all the time. An enemy cannot cause you quite so much pain as a friend.
The stare Garfield gives Jon, that makes him so uncomfortable, is administered on almost a daily basis. It is practically Garfield's default expression. The above communication, acknowledging as it does, that Garfield trademark derisive glare is as much for Jon's benefit as his own or ours, adds even further sadism to the last 28 years of strips. That Jon receives this treatment when only offering to have fun with Garfield, or offer assistance with light self-improvement (walking with your friend is probably the least taxing exercise possible), extends Garfield's reaction into mild overkill. Refusal is not enough, smart comeback is not enough. Garfield has to respond to an innocent question by pulling out a move designed to hurt Jon; the condescending stare-through is doubly-annoying because it's being employed after entreaties not to.
Garfield is trying to get across the relativist idea that what sounds "nice" to Jon may not sound nice to Garfield. All Jon ends up hearing is crickets, as Garfield's silent stare continues to burn through him. I'm reminded of the Beavis and Butt-Head Zen observation "I don't' like stuff that sucks"; Garfield inverts even the inarguable. In "You know how I hate nice walks," the implication is partly that somehow Garfield is so overwhelmingly negative that he's able to reject things that are empirically pleasant. Next time some one tells you Garfield is stupid, feel free to tell them that stupid is the new "brilliant."