"'One is not born a woman, but rather becomes one.'" 

Credited to Simone de Beauvoir, this quote references the idea of gender as something one does, rather than inherent trait resulting from some essence emanating from the body. Butler builds on this idea by positing that gender is performative. 

"Rather than a stable signifier that commands the assent of those whom it purports to describe and represent, women, even in the plural, has become a troublesome term, a site of contest, a cause for anxiety." 

One of Butler's central arguments is that the assumption of a coherent identity called "women" by feminists is an error because it ignores the inability of that identity to encompass the many variations of woman as a gender and because it’s based on exclusionary practices that undercut feminism's commitment to liberation.

"If the immutable character of sex is contested, perhaps this construct called ‘sex’ is as culturally constructed as gender; indeed, perhaps it was always already gender, with the consequence that the distinction between sex and gender turns out to be no distinction at all." 

Butler deconstructs the binary of sex/gender by pointing out that even sex is constructed by discourse/culture. Her insistence on seeing both sex and gender as constructed supports her later argument that there are more than two genders, and that our assumptions about the impact of biology on gendering tend to be wrong. Her use of deconstruction of binaries is an important analytical tool she uses to make her arguments.