I got an invite to Quora from a friend of mine a few months ago but the need for the FaceBook id was a killer. As long as they have this requirement, I won't use the product. Too bad really, because I hear good things about it.
After signing-up I could easily disconnect my FB account from quora account.
So, the logic of asking to sign-up using FB, does not really make a lot of sense - if its affecting user sign-ups.