Well, it would be PROFESSIONAL to explain why, but not necessary. Working holiday visas are good for either 12 or 18 months, depending on nationality, so I assume you have a job lined up back home. Just say that. You could also say that the one of you without a degree MUST leave because of the WHV expiring (and the other of you wants to return with the other person). No harm done.
Just realize that you will lose any year-end bonus by quitting early, and that could amount to reimbursing your airfare costs.