For more help, you may want to check out:
Selfish, Dishonest, Self-seeking, Frightened (afraid), Inconsiderate.
These five things are the core of what we do -- as a result of "thinking mostly about ourselves -- most of the time." (A simple description of "self-centeredness." ) . We've been living our lives as if "it's all about us" and that the world and everything in it "revolves around us." (We make it personal by personal-izing everything).
Self-centeredness is the thing that we're trying to be "rid of" and we must be rid of it entirely -- or it kills us, as alcoholics. It's the core of what feeds our mind into obsessional frenzy.
And, this is what it means to "be rid of Self". We can't be rid of Self entirely, or we would be dead. It's the "self-centered-ness" about ourselves that this refers to, in being "rid of Self."
I hope that helps.