Relationships as feature isn't a mutual connection. In this case it's more close to Following feature. It means that relationship created by "User A" to "User B"  isn't equal to relationship created by "User B" to "User A". 

For example, I want to list my relationships in my profile. I marked you as 'Brother', you should confirm that I'm your brother. In this case you'll be listed in Relationships block in my profile. In the same time you don't want to show your Relationships in your profile and won't espablish the same connection from your end. In this case Relationships on your profile will be empty. 'Relationships with Me' block shows relationships which were established by others and you may Reject or Confirm them there. Generally, the page from this screenshot is needed for profile owner to manage his own relationships and Relationships which he was mentioned in.