in most things, and suffering from an existential angst. He is less than thrilled--jealous, in fact--that his wife has invited to their home her blind friend, Robert. As he listens to his wife talk to Robert, he has resentment that she can speak of feelings and share with her friend things that she has not even mentioned to him.

After his wife goes on to bed, the narrator and Robert stay in the room where the television is, and they smoke some cannabis. When Robert asks the narrator to draw a cathedral that is being described by the speaker of the television program they are watching, the narrator finds a brown paper bag on which they can draw with Robert keeping his hand on top of that of the narrator. This act of creation becomes a meaningful spiritual experience for the two men, and the trust and friendship shown to him by Robert gives the narrator a new meaning to his life. 

“Well?” [Robert] said. “Are you looking?” My eyes were still closed. I was in my house. I knew that. But I didn’t feel like I was inside anything. “It’s really something,” I said.

For the first time, the narrator feels things, spiritual things, and he has had a meaningful experience.

This is a very open-ended and personal decision on your part; writing an interpretation essay on a short story will depend entirely on your interpretation of the piece.  In order to determine that, try asking yourself several questions.  What did I get out of this story?  What do I think that the author is trying to say?  What is the main point of the story and how does the author make that point?  If you think of some responses to that question, then that will lead you towards an interpretation statement that youc an use for your thesis.

I have provided several links below on writing essays, and on the story's theme and meaning, that might lead you in the right direction.  Take a look at those, as they will be useful.  In the meantime, to get you started, consider the following possible interpretations:  In Raymond Carver's "Cathedral," he is making the point that allowing yourself to put yourself into someone else's shoes is one of the best things that you can do.  Or, Raymond Carver, in his story "Cathedral," points out that empathy and perspective are the only way to truly experience profound emotion.  Or, In "Cathedral" by Raymond Carver, the main character discovers that to let go of his own rigid perceptions of the world is the most rewarding choice he can make.  So, those are some possible interpretations of the story that might work for a thesis statement.  Then, go through the story and find key quotes and passages that relate to that statement, and you'll be set to go!  I hope that helped a bit; good luck!

We would be doing you a disservice to actually write your thesis statement for you, but I can help you brainstorm a bit so that you can write your own thesis.  First, I assume that the two characters you are contrasting are the narrator and the blind man (Robert).  You might also include the narrator's wife if you want to include three characters, but you can certainly develop a solid contrast simply between the narrator and Robert.

Start by making a separate column for each character, and write their characteristics in the separate columns.  Look for a way to summarize the major difference you see in a single sentence.  Just to remind you, as the story begins, the narrator is narrow-minded, bigoted, and irritable.  Robert, on the other hand, is open-minded, outgoing, and expansive in spite of his blindness.  As the story develops, the simple act of tracing the cathedral brings these two men together.  Can you develop a strong sentence using these ideas?  I think you can.  Good luck.  Here is a good article that can give you some ideas for your thesis statement and your essay: http://www.associatedcontent.com/article/13368/blind_to_the_truth_blindness_in_raymond.html