How do the actions within the play prove Song's theory that all a man wants from a woman is to submit, and that will result in him recanting his demands?

Gallimard came into the situation hoping to gain absolute reign over his woman, but the guilt he felt for the possibility of gaining it from a woman he was not worthy of (much like Pinkerton with Butterfly) disgusted him. As soon as Song gave him what he wanted, he didn't want it anymore. If Song had denied him again, he would have forced the issue.