As Dr Grothe explains William Safire introduced the term contrapuntal to describe this reversal of the order of words, using an ABBA form, although there are more elaborate ones. The more common description is chiasmus.
For example Kennedy said: Let us never (A)negotiate out of (B)fear, but let us never (B)fear to (A) negotiate. You can probably remember the more famous Kennedy quote.
Joseph Kennedy also had a quote: 'When the going gets tough, the tough get going.'
The Mark Twain quote: "It's not the size of the dog in the fight, it's ...................
From the TaoTe Ching: Wise men don't need to prove their point, Men who need to prove their point aren't wise.
If you're like me, you will really enjoy this, and learn how to construct your own memorable little quotations.
What do Mae West, John F. Kennedy, Victor Hugo, and H. L. Mencken have in common? They all indulged in chiasmus-a literary device in which word order is reversed to hilarious or poignant effect. When Mae West said, "It's not the men in my life, it's the life in my men," she was using chiasmus; when John F. Kennedy said, "Ask not what your country can do for you, ask what you can do for your country," he was doing the same. Dr. Mardy Grothe has compiled hundreds of examples of chiasmus in this whimsically illustrated collection, bringing this witty and thought-provoking device out of obscurity and into the public imagination.