Derrida writes that there are two ways to interpret “the interpretation” of “structure, sign, and play."
“The one seeks to decipher, dreams of deciphering a truth or an origin which escapes play and the order of the sign, and which lives the necessity of interpretation as an exile.” In other words, this interpretation (Levi-Strauss's) seeks to determine an origin of truth that will have a stable structure with a certain center. The stability of this structure, with its immobile center, solidifies its truth in that it (namely the center) is always true and therefore always “present.” This sounds good in terms of defining truth but such a stubborn idea eliminates the possibility of interpretation and scoffs at the idea of change in time, space, and history itself. Levi-Strauss tries to account for this (and fails) by saying that he has provided an outline (structure) of South American mythology which may be subject to reinterpretation. Levi-Strauss's argument deconstructs itself because he proposes a general, universal (originary) structure and yet one that may be transformed.
“The other, which is no longer turned toward the origin, affirms play and tries to pass beyond man and humanism, the name of man being the name of that being who, throughout the history of metaphysics or of ontotheology—in other words, throughout his entire history—has dreamed of full presence, the reassuring foundation, the origin and the end of play.” In other words, this second interpretation of structure, sign, and play seeks to affirm play: the substitution of centers and structures.
For example, Levi-Strauss cites the “Bororo myth” as the “reference myth” which gives it a position of origin upon which the Bororo center some of their cultural traditions. As original, this myth would also have the definition of an origin, a center: something within the structure but, being unchanging, is somehow outside of that structure. But then Levi-Strauss says that this “key myth” is actually a transformation of other myths. Thus, he cites something as an origin and also an interpretation.
In challenging Levi-Strauss, Derrida explains that centers are subject to change just as other elements of a structure are. Therefore, he focuses on the differences, substitutions, and supplements of structures and centers. He does not seek to establish a set of stable, unchanging structures because he recognizes that, through time, history, and the function of language itself, change and difference are the natural and cultural functions of meaning.
In Levi-Strauss's thinking, there are structures that are essentially stable and therefore always present, always true in their always present “Being.” Derrida seeks to show how such a notion limits play. Play disrupts this notion of set unchanging structures. Deconstruction frees one from this insistence on the unchanging structural presence.
The "play" of the "sign" (word, myth, story, structure, center) is freed to change when we acknowledge that structures and their centers are changeable.