For one of the twentieth century's most influential anthropologists, Claude Levi Strauss did precious little field work and none of it would count as immersion into a particular culture. He was a theorist in a nineteenth century manner - absorbing vast quantities of material in his library and weaving from it a set of idea laden expositions that became recognised, unhappily for Levi Strauss, under the collective rubric of 'structuralism'.
Having read Patrick Wilcken's exceptionally well-written and informative intellectual biography of Levi Strauss (Claude Levi Strauss: The Poet in the Laboratory) that paints a vivid portrait of the man, his intellectual development and his context, I think I would remain hard pressed to say what 'structuralism' is (or possibly was). But, at heart, Levi Strauss did have a compelling core intuition that the human mind seeks order and that ordering (at one level) depends on binary thinking that focuses on the relationship (and difference) between things. Famously, for example, Levi Strauss' discussions of the 'raw' and the 'cooked' and it is in manipulating these binary relationships (often below the level of conscious thought) out of which is spun the complexity of a culture - whether mythologies, kinship patterns or the particular decoration of cooking pots.
Levi Strauss' analogy was a musical score where a certain set of rules (that could be analysed) generates an infinite variety of actual pieces of music but all of which can be illuminated through an understanding of the commonalities of their patterning.
The problem, it appears to me, is that Levi Strauss assumed that this particular way of seeking order was the 'primary' or indeed 'only' way of doing so; thus, anomalies to his binary structuring, within the ethnographic record, tended to be airbrushed out which he, and his biographer, tend to describe as 'nitpicking' but how much picking can a fabric takes before it falls apart? But, more importantly, it does not finally work on its own grand theoretical terms. Levi Strauss was fascinated at how music, for example, generates a whole field of felt meaning from the basic rules of ordering (which, as it happens, are n't binary either) but failed to notice that this very field of felt meaning was not simply in the ordering rules but between the rules, the generated music and the audience. It was in the field of which the listener is a dynamic participant not simply in the rules or the listener's understanding of the rules (of which he or she may, in fact, have none) and music finally only matters because it is heard and lived.
The self that Levi Strauss hoped to erase from the equation - leaving one simply with the elegantly analysed rules is instead an integral part of any patterning.
This tendency of a part of the mind to achieve necessary objective ordering and yet immediately, and falsely imagine it is the only possible ordering, is brilliantly investigated in Ian McGilchrist's 'The Master and His Emissary' (see http://www.iainmcgilchrist.com/) and brings us back to the critical question that Levi Strauss simply evades - what is the nature of the mind that is knowing and how flexible is that mind to achieve different levels of knowing? Any ordering is a skilful means for addressing certain questions, an enterprise after a particular kind of knowing, but not necessarily the only means. The relationship between the means adopted and any notion of the truth of things remains in abeyance in Levi Strauss - indeed he thought it a redundant question - but in adopting only one manner of ordering, he left so much 'surplus' reality unaccounted for that the question is very much still alive and kicking!
It is a question that, ironically, the indigenous people Levi Strauss was busy studying would have taken for granted - they are notable pragmatists - this is knowledge we need but recognise others might need different knowledge and beyond any particular ordering may be deeper unities to which we may have access if we access different states of consciousness. It is one we seem to have inordinate difficulty with in these three provincial centuries (to quote Yeats) with addressing at all. This taken for granted has become 'erased' (to use a post structuralist expression) and our mind has arbitrarily limited its own structuring (and indeed potential restructuring)!