MRS. CHEVELEY: Ah! The strength of women comes from the fact that psychology cannot explain us. Men can be analyzed, women merely adored.
SIR ROBERT: You think science cannot grapple with the problem of women?
MRS. CHEVELEY: Science can never grapple with the irrational. That is why it has no future before it, in this world.
SIR ROBERT: And women represent the irrational.
MRS. CHEVELEY: Well-dressed women do.
This exchange takes place toward the beginning of the dinner party in Act I before Mrs. Cheveley moves to blackmail Sir Robert. As one of the primary themes of the play consists of competing visions of womanliness, it is of interest in that relating aestheticism with a certain conception of femininity.
As discussed in the Context, aestheticism, a doctrine often abbreviated as a philosophy of "art for art's sake," insists on art being judged by the beauty of artifice rather than that of morality or reason. Beauty is irrational and amoral, and the aestheticist who worships beauty indulges in excess and exaggeration to flout his age's standards of respectability (i.e. "proper" thinking, proper aesthetic and moral judgments, etc.).
Typically one imagines the (male) dandy as the epitome of the aestheticist credo: artificial, amoral, and irrational. At the same time, like the dandy, these terms are often associated with the feminine. Here Mrs. Cheveley poses woman as a sort aestheticist art object. Like art, women can only be adored—that is, not analyzed—and herein lies their strength. As objects of admiration, women resist judgment according to rational or moral categories. They embody the irrational (or at least when well-dressed) and are thus powerful, perhaps even dangerous. Mrs. Cheveley herself is of course one of these dangerously well-dressed and irrational women.
If female strength lies in the irrational, one might note that Mrs. Cheveley's wit draws from the irrational as well. In this instance, irrationality inheres primarily in her use of hyperbole and false logic: if men can be analyzed, women can only be adored; science has no future in the world. Such irrational speech is what makes Mrs. Cheveley such a mighty conversational foe, poised to manipulate her interlocutors and misconstrue situations to her own advantage.