Chiasmus is the reversal of grammatical structure across two parallel clauses: the second half mirrors the first, running its elements in the opposite order. The shape is ABBA, and the reversal is what the reader notices, even when they could not name it.
The figure implies a relationship of balance or exchange between the two halves — that one is the counterpart of the other.
Kennedy, in his 1961 inaugural: “Ask not what your country can do for you — ask what you can do for your country.” The same six words, reordered. The reversal enacts the shift in obligation that the sentence is arguing for.
Kennedy's line is strictly antimetabole — chiasmus in which the exact words are repeated, not merely the structure. All antimetabole is chiasmus; most chiasmus is looser.
Chiasmus is unusual among rhetorical figures in that the structure carries meaning rather than merely decorating it. A reversal implies symmetry, and symmetry implies that the two halves are genuinely counterparts — equal, exchangeable, two faces of one situation.
That implication is doing real argumentative work, and it is rarely examined. “We do not stop playing because we grow old; we grow old because we stop playing” is memorable precisely because the reversal sounds like a discovery. But reversing a sentence does not establish that the reversed version is true, and chiasmus is capable of making a causal claim feel proven simply by being well shaped.
The device is also nearly impossible to use twice in the same piece without the reader noticing the machinery. Its memorability is concentrated: one chiasmus is quoted for a century, two in the same speech sound like a trick.
When you meet one, the useful question is whether the second half would stand on its own. If it needs the first half's symmetry to seem plausible, the shape is carrying the argument.