By saying, "Why do you think this is the case?" you are asking the person to explain how or why the situation in question came to be. You're asking what that person thinks has caused the situation, or led to the situation.
Example:
Person 1: My sister isn't talking to me.
Person 2: Why do you think this is the case?
Person 1: Because I stole her clothes.
Example 2:
Person 1: I feel sad today.
Person 2: Why do you think this is the case?
Person 1: Probably because I'm lonely.