What the question your parent poses can do is get to the root of the objection your conversation partner has. "What would make you change your mind" forces the conversation in the direction of uncovering the true source of the disagreement. It helps to avoid talking about "symptoms" or issues that you might find important but are not important to your partner. It helps avoid talking past each other. It helps identify what issues are important to the other person.

If there is nothing that will change one's position, it's not worth engaging because the outcome is set.