We learn right off the bat that the older man at the center of "Why Don't You Dance?" likes his whiskey. From there, it's hard to find a moment in the story where he doesn't have a drink (or two) in his hands. On top of that, his hospitality to his young guests/potential buyers consists primarily of getting them totally wasted. So yeah, alcohol is pretty central to the story and its events and not in the healthiest way.
It's clear that the older man has just lost his wife, and his hard drinking seems like it might be related to his pain over this loss. The frequent references to alcohol and drinking definitely add to the feeling that the characters are beating off unhappiness with a stick—or a stiff drink, as the case may be.
These guys are just partying. Alcohol represents a fun release for the characters from their day-to-day problems.
The constant alcohol use throughout the story is definitely a signal that these characters—and the older man in particular—are in a seriously bad place.
The premise of "Why Don't You Dance?" is that a dude has somehow lost his long-term lady companion, and his response is to put all their shared furniture out on the lawn and up for sale. As a result, the story asks readers to start thinking about love and relationships right from its opening lines.
There's also the fact that a young couple—two kids just starting out together in life—show up to buy the older dude's furniture, which makes us (the readers, that is) think about relationships even more.
The story doesn't exactly offer a warm and fuzzy presentation of love and relationships. The older man is obviously in some kind of pain or turmoil after losing his wife, so that's a given for him. As for the younger couple, we're not quite sure what's going on with them, but given that the young girl ends up being attracted to the older man's "desperation," we're not super sure there's a bright romantic future in store for them, either.
Carver puts two different relationships at the center of his story to suggest that love often involves unhappiness and/or seamy behavior.
The relationships in this story (and the fact that we get little backstory on them/the people involved) highlight the idea that other people are puzzles that will never be solved—it's just plain hard to understand other people.
The premise of "Why Don't You Dance?" is that all the older man's stuff is up for sale, so there's quite a bit of chatter about money. The young couple shows up early in the story while the guy is out, and starts strategizing how to get the most stuff for the least amount of money. It's kind of sad since this guy is basically selling his entire life away, and the couple is trying to lowball him on the souvenirs and objects associated with that life.
The older man doesn't seem to care, though—he's perfectly happy to accept whatever price the kids want to offer him. The fact that he's so happy being lowballed shows just how desperate he is to shed off his former life… or perhaps for something else this young couple offers him.
"Why Don't You Dance" kind of gives us the creepy crawlies—there's just something off about the characters, what they're doing, and what they're willing to let other people see them doing. In particular, the older man and the young girl seem perfectly willing to engage in unorthodox behavior, but there's also the sense that they feel self-conscious (or know that they should be feeling self-conscious) about their quirky ways. In other words, the characters suffer just a tiny bit from guilt/shame/self-consciousness regarding their choices—but those feelings don't stop them from acting anyway.
The story highlights this whole idea of being watched to draw attention to how self-conscious the older man must be feeling in his little neighborhood with his relationship having ended.
The story plays with feelings of guilt vs. feelings of, well, non-guilt to foreground that the older guy is a creeper. The fact that he is so willing to put his life and "desperation" on display indicates that he's an unsavory character.