Ugh, I think people are putting to much of their personal life on Facebook, which makes it easier for them to get caught. I also can't stand when couples give their login to the significant other. I mean some things should remain personal.
The appropriate response to such a question is, "No. And it creeps me out that you would even ask." Arguments about having nothing to hide are countered with "You have no reason not to trust me. It seems like you might not. And if that's true we have a major problem." You know your own state. You know if you're being (or have been) a weasel. If your state is clean and someone acts like this consistently it is psychological projection (or some other show-stopping psychological issue). Beware of such people.
"4. Registration and Account Security
...You will not share your password, let anyone else access your account, or do anything else that might jeopardize the security of your account..."