A former alcoholic, Raymond Carver knew well what alcohol can do to personal relationships. We'll give you a hint: nothing good. And "What We Talk About When We Talk About Love" is no exception to that rule. We've got drunk driving, drunk arguing, and drunk sitting in silence, stewing. As the characters grow more and more drunk, their conversations become more incoherent and frustrating. Mel, of all the characters, struggles the most with his gin-soaked words, and the more he tries to explain love, the more we think that alcohol has nothing to do with it.
By lowering their inhibitions, alcohol allows the characters to have an intimate conversation about love, something they might not ordinarily feel comfortable talking about.
Alcohol is nothing but bad news in this story, because it causes Mel to become less coherent and more belligerent. The harder he tries to define love, the farther away he gets from an actual answer, and the gin is to blame.