An antagonist is the character, idea, force, or even setting that opposes the protagonist; in other words, the antagonist need not be a character at all, and if it is, he or she might be a figure of good if the protagonist is a figure of evil. With this in mind, you might consider if the antagonist in “Cathedral” is that part of the character that keeps him closed minded, cynical, and without empathy, for the story is all about him overcoming those flaws to be a fuller human being when, with the help of Robert, who cannot see in a literal sense, teaches the narrator to see in a new way, by connecting to another person. He says at the end that he “didn’t feel like [he] was inside anything,” suggesting that by drawing the cathedral through touch, he breaks down the rigid boundaries of self that isolated him from emotional experience.
The narrator's wife is the antagonist in the story. She and her husband have a distant relationship, with no warmth or sharing between them. The narrator has isolated himself from everyone, and he even resents his wife's ability to communicate with people. She was lonely and isolated in her first marriage and tried to committ suicide. It was only because she kept in touch with Robert that she was able to overcome her feelings of death. Her marriage to the narrator doesn't provide her with the comfort and love she needs, and she must look for human contact elsewhere. She doesn't feel her husband loves her, and she begs him before Robert's arrival to behave appropriately to Robert. "If you love me...you can do this for me. If you don't love me, okay." In the end, the narrator and his wife have hope that their lives will change because of Robert's caring, kind nature. The narrator and his wife should be consoling Robert because of his wife's death, but it's Robert who ends up making the couple feel better.