I don't think I know one person that hasn't fallen victim to the desire of being in the inner ring. As C.S. states, it's unavoidable.
Thought looking back on it, one of the lows of my life was when I picked up and left my group and my circle and my life as I knew to join another ring that, at the time, seemed more esoteric. Though truthfully, the only esoteric quality this new ring had was that we all thought of the my other ring as less. Other than that, they fell very short of satisfaction the whole way around.
But giving into this desire of being in the center ring, opens us to giving in to more desires. Like C.S. Lewis says, how many layers of an onion can we peel? Eventually, we'll have nothing left. If we join a ring for the sole purpose of wanting to be admitted we'll lose that desire and gain no satisfaction because how can we desire to be apart of something we already are apart of? If we joined for the activities the group is founded on, we may get some satisfaction of it.
I think this all points to another of C.S. Lewis' concepts. We just can't be satisfied with anything here on earth. We get glimpses. But most of the time we are more satisfied with yearning for satisfaction. An odd, circle of a thought, isn't it?