How can a mediator "invent" options to settle my case?

In "Getting to Yes", by Fisher and Ury, a story is told about two sisters who argued over who was to get the last orange in the kitchen. They settled by cutting the orange in the middle and each took her half. One sister took her half orange in the den, ate the fruit, and threw away the peel. The other sister stayed in the kitchen, used the peel to make marmalade, and threw away the fruit.

Each sister liked to yell at her sister, and they did settle, but with a little mediation and a discussion of what they really wanted, each sister could have had all she wanted.

Not all problems can be mediated by asking, "Why?"
Not all problems can be mediated by asking, "What is the real deal?"

However, by asking the right questions, and using the other tools at his disposal, a mediator should offer options to the parties that makes the settlement possible.