That's what one-way hash functions are for. You never store the raw fingerprint data, just its unique salted hash so the data cannot be reused elsewhere.
It only takes one place where security standards aren't implemented properly to have your print leaked forever.
Never mind a malicious user managing to alter the code to leak the print before it's hashed.
Or even someone physically accosting you and retrieving a brain scan. They could do the same thing and force you to give up a password, but at least the password you can change later on.
For that matter, a password is always your choice to reveal or not, taking the cost and alternative into account. Biometric information isn't.