Antimetabole
Etymology
From Greek "antimetabolē" (a turning about), from anti- "against" and "metabolē" (change), from "metaballein" (to turn about). A named figure in classical rhetoric.
noun · /an-tih-muh-TAB-uh-lee/
The repetition of words in successive clauses in reverse grammatical order.
What it names
The device behind the most quotable lines in oratory — reach for it to name the mirror-flip of "ask not what your country can do for you; ask what you can do for your country."
Example
"When the going gets tough, the tough get going" owes its stickiness to antimetabole.
Related idea
Often confused with chiasmus, which inverts the structure or ideas of a phrase; antimetabole is the stricter case that repeats the very same words in reversed order.