Post-structuralism emerged in the mid-to-late 1960s, became popular at Yale University in the 1970s, and began to spread like wildfire across American campuses in the 1980s, the decade it is most strongly associated with, although it is a product of the '60s and post-World War II consciousness.
Derrida is often credited with starting the post-structuralist revolution with his essay
"Sign, Structure, and Play in the Discourse of the Human Sciences." In it, he leans into Levi-Strauss's insights about anthropology. Anthropology had long held that human behavior fell into two distinct and rigidly separate categories: behavior was either cultural or biological (natural). However, Levi-Strauss noted, incest taboos defied that binary categorization: they were both biological/natural (shared by all cultures) yet culturally distinct (different cultures banned different kinds of incest).
From this, Derrida realized that what we perceive as foundational truth is simply provisional. What we base our theories of knowledge on is what he called bricolage, or what today might call a kluge—basically, whatever is on hand to support the structure of thought we are constructing. It is as if we needed a support beam for our house but couldn't find one the right size, so we improvised and stuck in whatever worked, shoving twigs and newspapers in the gap; after all, you have to have a house.
Therefore, since the foundational truths on which we structure knowledge are provisional, they will change and be discarded once they are either no longer useful or something better and more solid comes along.
This insight rocked and revolutionized academics. People were simply overwhelmed and stunned: the binary oppositions, such as nature/culture and male/female were simply kluges? This insight couldn't have hit at a more opportune cultural moment, as the late '60s were already rocking with challenges to orthodoxy.
Derrida and other post-structuralists with similar reformulations to the "way things are" laid a foundation for feminists to challenge foundational ways people structure thoughts about gender and foundational ways for post-colonial peoples to challenge the structure of thought that oppressed them. Everyone began to rethink what they thought they knew. The world would not be the same.