Facebook has only two options for choosing who can send friend requests: everyone, and friends of friends. This means I should be able to send a friend request anyone that is a friend of a friend. However, I've seen a couple of mutual friends that don't have the "Add friend" button. How is this possible?
I have seen that too. What that means is they have set their security settings so high that people are not able to request to add them as a friend. I found a dear old friend on FB but unfortunately, they had both the "add friend" and "message" buttons not available due to security.
Many people don't realize what they have done with these settings.