In this case your account probably was not locked, you just needed to provide additional information to log in because something seemed unusual. So if you logged in from a known-good environment (ie, a computer we know you have logged in before), it would work - you aren't locked out of your account.
This is one of a few different systems we have to protect our users - in this case from having their credentials used if they are exposed through others sites, through phishing, or through some other mechanisms. You can a little about it at https://blog.facebook.com/blog.php?post=389991097130
If you are concerned about privacy, but not happy about having to log in from scratch each time and occasionally have to go through these steps (or not comfortable giving or not able to give a phone number for text message authentication), you might want to use a separate dedicated browser for Facebook that does have cookies enabled.
This is one of a few different systems we have to protect our users - in this case from having their credentials used if they are exposed through others sites, through phishing, or through some other mechanisms. You can a little about it at https://blog.facebook.com/blog.php?post=389991097130
The social authentication is one way we help people verify their identity in these cases - you can read about it at https://blog.facebook.com/blog.php?post=486790652130 . There are others - the easiest for most people is through sending a text message to your phone when you log in from a new device, which you can read about at https://www.facebook.com/note.php?note_id=10150172618258920
If you are concerned about privacy, but not happy about having to log in from scratch each time and occasionally have to go through these steps (or not comfortable giving or not able to give a phone number for text message authentication), you might want to use a separate dedicated browser for Facebook that does have cookies enabled.