When you logged in the first time, and used your Security Key or YubiKey at that time for two-factor authentication, you selected the option to Remember Browser. This is a feature that Facebook is using with the built-in capabilities of your browser. A cookie is issued after you have authenticated, and it’s used to remember that you have logged into Facebook previously.

To force the requirement to use your Security Key or YubiKey when you login each time, go to Settings > Security > Login Approvals, Recognized Devices, and remove the browser you are currently logged in with.

in FacebookFrequently Asked Questions