The answer to the question of why they all confess lies at the heart of the objective of the tale, which is to show that people are guilty of morally compromising themselves. In the story, the moral compromise leads each character to tell events with a slant in their favor, even the ghost of the dead Takehiro. Rather than face their own self-originated humiliation, each changes the truth somewhat. For instance, Masago doesn't want to confess that she was willing to abandon her husband and instead become the husband of the villain Tajōmaru because that is too humiliating. She would rather confess to a pact of joint-death murder than be exposed as disloyal.
The ambiguity of facts at the end of the story leaves that reader in the same position as the characters. The tale doesn't give enough facts to logically determine which person stabbed Takehiro, and even his ghost is unreliable, as his evidence doesn't explain all the facts. Nevertheless, even though the reader can not ascertain truth, almost invariably a determination is made of who is guilty and who innocent based on a preconception of sympathy with one character's or another's trustworthiness, or believability. This morally compromises the reader because the choice isn't made on fact--it's made on emotional preference.