The word "religion" points to that area of human experience where one way or another we come upon Mystery as a summons to pilgrimage; where we sense beyond and beneath the realities of every day a Reality no less real because it can only be hinted at in myths and rituals; where we glimpse a destination that we can never fully know until we reach it.
Since the Reality that religion claims to deal with is beyond space and time, we cannot use normal space-and-time language (i.e. nouns and verbs) to describe it directly. We must fall back on the language of metaphor and resign ourselves to describing it at best indirectly.
It is obvious that this is what we are doing when we say Jesus is the "Son of God," or the Lord is our "shepherd," or the Kingdom of God is "within you." It is not so obvious that this is what we are doing—but we are doing it no less—when we say, "God exists." This does not mean that God "exists" literally as you and I do—that is, exists now and not then, here and not there, and stands out of (ex + sistere) some prior reality. It is at best a crude metaphor.
To say that God "does not exist" may be a better metaphor to suggest the nature of God's reality. But since it also is bound to be taken literally, it is better not to say it.