If you ask somebody “Can you open the door?” and he answers “Yes” but does not actually do it, what would be your reaction? Why? Try to see it in the light of speech act theory.
I would be angry with him. “Can you open the door” is normally understood as a request of the hearer to do it rather than a question about his ability. The fact that he answers “yes” but does not actually do it shows that he declines my request.