At the end of chapter 3, Nick asserts that Jordan lies. In particular, he suddenly remembers an incident of barely averted scandal in which she was accused of moving a golf ball to a better position during her first tournament. He writes that she was "incurably dishonest."
He also recounts a time in which she drove carelessly. When he accuses her of almost running over a workman on the side of the road, she responds that she doesn't need to be careful because other people are.
Nick notes a further incident that illustrates both her carelessness and dishonesty: she leaves the top of a "borrowed" car down in the rain and then lies about it.
These incidents, if true, show that Jordan puts protecting herself above being honest; it's more important to her to look good (like a winner at golf and like a person who is careful enough to put a car top up) than to tell the truth. It has often been suggested that she engages in subterfuges because she is gay, needing to
keep that cool, insolent smile turned to the world and yet satisfy the demands of her hard jaunty body.
Because Jordan can't defend herself or argue with what Nick is saying about her, the words say more about him than her. He shows his sexism when he makes a blanket and derogatory statement about "women" in general:
It made no difference to me. Dishonesty in a woman is a thing you never blame deeply—I was casually sorry, and then I forgot.
The passage, including the above statement, also shows Nick's dishonesty, at least to himself. Obviously, everything he says about Jordan did make a "difference" to him or he wouldn't dwell on these traits long after the fact. He also, obviously, didn't forget. Further, although he says honesty is his own "cardinal virtue," he carelessly makes this statement just after he has explained that he has been dishonestly leading on the girl in Chicago to whom Tom and Daisy thought he was engaged. All of this suggests that Nick is blind to some of his own flaws—and perhaps projecting them onto Jordan.