What does it mean when a person cannot answer a simple yes or no question They answer elaborately but still not answering the question?

They might fear offending you, or they might not be sure, or it is possible that a simple answer doesn't actually mean anything in this case.

For instance, if you ask a man who has never abused his family, "Have you stopped beating your wife?," a simple yes or no answer isn't sufficient. He needs to present more context and help you understand that the question itself is invalid.