The song covers status, respect, sexual availability, and so on. As we are not barnacles, the proper environment of Man is Man. Forget the deserts and the prairies, the jungles or tundra. We live with others of our species first and foremost, and that in turn means hierarchy and its hangups, position and its privileges. The Inner Ring gets you companionship, a stronger support network, and a greater availability of opportunity (social, romantic, professional). Outside of it and you're left scrabbling for the same things.
I saw it in grade school and then high school. I went to college and I found an Inner Ring among the students who all decided to live in the A-Frames; their social graph was incredibly dense and, when I sleuth through Facebook years later, has yet to be fully teased apart. It has arisen anywhere I have worked where sufficient numbers of people existed. Once you pick up on it, it shows itself over and over.
Now, I disagree with Lewis largely over his attempts at consolation via some kind of nebulous and unspoken (even unconscious) runner-up respect for not having compromised ones values or some nonsense, a bit like a Promised Land to which the faithful will eventually be granted entry. It's the usual Christian refrain of "You will have wealth ... in your heart." At worst, it's a kind of "stay in your place" classism, designed to keep the credulous recipient of this "wisdom" passive. Generally, when you hear about some virtue and notice that possession of this virtue benefits others, and you hear about this virtue from others, add a little suspicion to the mix before you swallow it whole. Being staid and unstriving is certainly convenient for some people, other people.
Lewis was almost certainly of an Inner Ring himself, given what you read of his contemporaries, so in a more cynical sense, he is attempting to keep that Inner Ring small (one of the commandments of being in an Inner Ring is that one must not allow in riff-raff) by suggesting that desiring leads to some flavor of moral compromise and you've got the nice parallel that craving leads to suffering.
Quite a lot of people have a vested interest in keeping you where you are. Remember that when you hear someone pooh-poohing some social or financial upward mobility. We can't all be nobility, so let's have the suckers filter themselves out.