I started my teaching career in Raymond Carver's high school in Yakima, Washington, so greetings from Carver country. I'll assume you are referring to the characters in Raymond Carver's story, and how alcoholism affects them throughout.
Carver himself was an alcoholic for the better part of a decade, and it ruined one of his marriages and estranged him from his children for a time, although, from that time period come some of his most profound writings. In this case, he is writing from experience and weaving that into What We Talk About When We Talk About Love.
The four people in the story certainly get more honest as the booze starts to flow. It unveils their insecurities and anger. It allows them to say things that they would not sober. The key to the story comes at the end, when Mel dumps his entire drink over on the table. There is nothing more to be said in the conversation, and so, no reason to continue drinking. The Gin, in this case, is the difficult conversation.