Why does Nick think Daisy's cynical outburst is fake?

The look in her eyes and her actions are in direct opposition with her words. Nick believes her to be completely insincere.

"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 exact a contributory 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."