Why do you have to sign in with Facebook on WikiAnswers when not everybody uses Facebook?

Actually, this is no longer true. Facebook is not required for logging in anymore. You can now sign up with just your email.

The reason Facebook was required was because the users were already vetted in advance. Vandalism was quite high, and the worst of users would likely be kicked off of Facebook before being able to abuse this site. Like this site, they require users to be 13 and older to participate, so the odds of discovering underage users is greater when requiring Facebook, since that would mean more people to report ineligible users. Now, with the layout change, certain types of vandalism are no longer possible. The regular users have less abilities now and have to get a badge like the Trusted Contributor badge to do what used to be possible without it. So that means they are free to do away with Facebook and allow more people to directly join. That makes the site more accessible, and the system changes still keeps the vandalism to more manageable levels, even with the registration increase.