So, let me see if I understand correctly...
You can add someone to your "Fan Of" tab without that person's consent.
You can attempt to add someone as a "friend," but for it to happen, the person has to accept your invite.
You can add someone to your "family," but first, you must have made a "friends" connection with that person.
You can't add someone to your list of fans (which makes sense) - that tab shows who has added you to their "fan of" list.
Following along so far? Good. Let's continue...
Removing someone from your "friends" tab will automatically remove you from that person's, but it will not automatically break a family or fan connection. An important note, especially for those people who have sexy pictures up with an access level set for Family Only.
You can drop someone from your "Fan Of" tab, but that person has to drop you manually if you want that person to disappear from your list of fans. This part bothers me. Unfortunately, I've had to use the block feature on certain people, yet they still show up as fans. Worse, since we've blocked each other, there's no way to tell the other person "please remove me" if I don't want to see their face on my Fans tab. What is worse is that I haven't been able to test if this person still has access to read bulletins that are addressed to "Friends and Fans" (as opposed to "Family").
I guess this is one of the many nuances about LC's contact list that I'll have to clear up at some point. I guess I'll talk about it some more after I've done some more digging.