Here's what I figure: Corner knew that my Mother would know about his blood-status because she's one of the organisers for Sons of Wizardry and Sisters in Witchcraft. So it probably occured to him that I would eventually find out the truth from her, and that I would then tell Teddy, and then he'd lose Teddy's friendship as a result. So he decided to confess to the truth before any of that could happen, hoping that it would make him look better. And plenty of people fell for it, too.