I associate the song very much with the movie "Alfie", whose title character is a heartless cad who bulldozes over others' feelings. I hear the singer asking Alfie if, as he seems to believe, life belongs only to strong people like him ('strong' meaning 'not given to sappy emotionality' - a plus for Alfie, a big minus for the singer), then what does he make of, or what can he contribute to the golden rule ("do unto others")? The singer answers the question for him, that only when we learn to love others do we really live fully.
I think this is one of the most original and beautiful pieces of music Bacharach has written - and that's saying a lot. But I always particularly associate it with Hal David. I can't speak for him, of course, but I always feel as though I hear his voice very clearly in this song, especially in the "As sure as I believe..." line.