What We Have Now
Imagine for a moment that you are in a desert. Not just what we experience outside of this town we live in, but an emotional and spiritual desert in which you feel isolated from others. Where you feel that you are alone, with no one to talk to, and nothing that feeds your soul with freshness or joy. Imagine that you are in this place, and now think of what would be your biggest desire.
For most of us, it would likely be that we would want to be anywhere else but that desolate space. We would believe that what we are experiencing now is not what we should be experiencing. That anyplace other than this desolate wilderness is better than where we are now.

The Way Home
So, to me, for someone to say that they are “spiritual, but not religious,” means that they are saying something to the effect of “I’m a human being.”
Of course, I’m being deliberately obtuse with my own question, because what people generally want to convey with that statement is that they simply do not subscribe to any form of organized religion, and prefer to find their own method of making sense of the world; that they do not find any meaning in the structures others have created, but prefer to create their own order within the chaos.