Daisy's cynical outburst occurs in Chapter I as she talks to Nick about her life since her marriage, telling him that she had had "a very bad time" and that she was "pretty cynical about everything." She describes the birth of her daughter and follows that sad recitation by telling Nick that she thinks "everything's terrible anyhow." After explaining that she has "been everywhere and seen everything and done everything," she concludes somewhat defiantly by declaring, "Sophisticated--God, I'm sophisticated!"
Nick's reaction, his assessment that Daisy's words constitute a performance on her part rather than an honest expression of feeling, follows immediately in the text:
The instant her voice broke off, ceasing to compel my attention, my belief, I felt the basic insincerity of what she had said. It made me uneasy, as though the whole evening had been a trick of some sort to extract a contributary emotion from me. I waited, and sure enough, in a moment she looked at me with an absolute smirk on her lovely face as if she had asserted her membership in a rather distinguished secret society to which she and Tom belonged.
In these three sentences, Nick identifies Daisy's basic insincerity and her flair for drama.
As said above, the three sentences that suggest that Nick thinks Daisy's cynical outburst is fake are as follows:
The instant her voice broke off, ceasing to compel my attention, my belief, I felt the basic insincerity of what she felt. It made me uneasy, as if the whole evening had been a trick meant to extract a contributary emotion from me. I waited, and sure enough, in a moment she looked at me with an absolute smirk on her lovely face as if she asserted her membership in a rather distinguished secret society to which she and Tom belonged.
The background to the passage is a small dinner party gone awry because Tom has gotten a phone call from his mistress. Daisy clearly knows he has a mistress, though she doesn't know who it is. Nick is trying to cover up the awkwardness by engaging her in conversation about her child. She resists his obvious attempts to get her to say the right things about the glories of motherhood and instead conveys her unhappiness, saying she hopes her daughter will be stupid and going on to talk bitterly about sophstication.
The passage is significant for several reasons. First, the siren-like magic of Daisy's voice will recur throughout the novel. The way she says things seduces. Second, the "secret society" Nick mentions foreshadows the ending, when it will become obvious that whatever marital difficulties they have, Daisy and Tom also have an inviolable bond. As she does here with Nick, Daisy will also use Gatsby.