A conflict arises with the confrontation of two opposing parties. Generally the conflict includes the protagonist pitted against an antagonist, whether it be represented as his conscience, nature, God, society or self.
In "Cathedral" by Raymond Carver, the conflict is man vs self. Robert, an old blind friend of the narrator's wife is coming for a visit. His wife has recently died. The narrator is angry that the man is coming and is hostile toward him. At first it seems that he is jealous of the attention his wife is giving Robert. However, I believe that the conflict is within the narrator, not with Robert. The narrator has certain perceptions about Robert, his wife, how Robert should act, how the narrator should fit into the picture, etc. The problem is his own; but throughout, Robert is very gracious about it all.
Because the conflict is man vs self, interestingly, I find that the antagonist is the narrator—or more specifically, his anger with Robert, which may simply be a manifestation of his frustration with the world around him.
Lilia Melani provides the following definition for "antagonist:"
The antagonist is the opponent; the antagonist may be society, nature, a person, or an aspect of the protagonist.
This makes perfect sense in light of the conflict of man vs self. It is not until the narrator can "let go" of his anger with Robert and the world that he finally is able to resolve his hostility. (His anger and hostility are the "aspect" of the narrator that acts as the antagonist.
Robert talks the narrator into drawing with him—having the narrator's hand guide Robert's. It is not something that the narrator had expected. He follows Robert's directions, but feels like what they are doing is crazy.
So I began. First I drew a box that looked like a house. It could have been the house I lived in. Then I put a roof on it. At either end of the roof, I drew spires. Crazy.
Robert and the narrator continue to draw and Robert praises the narrator's work even though, ironically, Robert cannot see what the narrator is drawing, but he can feel the deep impressions the narrator makes on the paper. However, perhaps the picture is not what is important at all, for he tells the narrator:
Never thought anything like this could happen in your lifetime, did you, bub? Well, it's a strange life, we all know that.
This may summarize the narrator's difficulty. He has lost his ability to hope and imagine. He has less "vision" than Robert, and in this exercise, the blind man is leading the blind man: though one is blind figuratively (the narrator), while the other (Robert) is blind literally.
As the narrator starts to realize possibilities that emerge on the paper in front of him, he finds he cannot stop. All the while Robert is encouraging his companion. Sleeping on the couch, the narrator's wife wakes and wants to know what they are doing. Robert has to explain, for the narrator still cannot stop—doesn't speak. And still Robert praises him:
You didn't think you could. But you can, can't you?
Then Robert tells him to draw with his eyes closed. This would seem impossible to do. But the narrator does it: he does the impossible, and he notes:
It was like nothing else in my life up to now.
The eNotes summary puts it quite nicely:
Something has happened to him that has changed his understanding of life...No longer hostile to Robert, no longer aware of Robert's blindness, the narrator experiences the possibility of change in his life.