I would use either "can't" or "don't" see for the unspied bird with little if any distinction. I would also use either for an argument but "don't" would imply a lack of understanding and "can't" an understanding but disagreement as to the validity of the argument. There would probably be other differences, e.g., "I don't see what you're getting at," vs. "I can't see it that way."

As an aside, in my youth I had some contact with a number of blind people. They all pretty much used "see" in the figurative sense. There was no discomfort using the term with them if you understood this.