Who was “that man”?

Among the Methuselahs of riddledom few present themselves for solution more frequently than the following brain teaser: “Brothers and sisters I have none, but that man’s father is my father’s son.” The average person will reply by saying incorrectly that the man is the person speaking. But the riddle cannot be so construed. It refers to a father (an only child) speaking of his own son, that man being the son of the speaker.