A reality of working with people is the periodic need for difficult conversations. Using storyboards allows the author to more easily predict how the other person will respond due to the conversational nature of the storyboard format. More time spent planning increases the chance of a successful resolution. Storyboards are also helpful when mentoring someone: walking them through a difficult conversation to help them see both sides of a situation.
Pro Tip: Sharing your storyboard with a third party often helps tone down the approach from confrontational to collaborative.