As a Movie Guy, I admit I don't think there's anything inherently wrong with any genre, even the "chick flick". The genre formerly known as "women's pictures", with a long and illustrious history from Now Voyager to Love, Actually, may not be Jon's ideal Friday night entertainment, Davis hasn't gone out of his way to identify a specific torturous film. Jon is indeed the target audience, a young man on a date, and even if he doesn't find something to enjoy in the movie, he may make good by Liz and the genre is pretty inoffensive anyhow. We've seen Jon mention a love for children's films, and settle in for an evening with Brigette Bardot movies; while there's plenty to sustain male interest in a Bardot picture, most of them aren't Dude Movies par excellence. Choosing a date movie is tricky business anyhow, and most would agree a healthy ability to suck it up and let your date indulge their interests is a good thing. I spend this time to illustrate that it's not Jon's behavior at the heart of the joke.
Garfield witnesses one of the small compromises that happens in all relationships, and gives it a thumbs-down. Granted it is not just Jon's willingness to spend Friday night at a movie he doesn't want to see in exchange for time spent with someone he cares about that Garfield views as emasculating, but Jon's blissed-out zombie state confession that small nuisances don't bother him right now. Garfield's stubborn self-centeredness causes him to draw a hard line in all things: the cat will never do anything he does not want to do, and when his back is against the wall he will sabotage the situation (e.g.- constantly abusing Odie) or complain about it (e.g.- everything Jon does every day). Garfield cops a song title from Cinderella for his sarcastic refrain. It is a song which celebrates approximately the state in which Jon finds himself. Days like this both the guys might be right, but the thing about cynics is they think they're realists.