Antimetabole: Balancing one clause against another by reversing the grammatical order of the second clause, making the second clause a grammatical mirror-image of the first . See also chiasmus.
While no one should be dying to eat, neither should they be eating to die.
Never mind how life is treating you; how are you treating life?

A famous example from a JFK speech:
Ask not what your country can do for you, ask what you can
do for your country.

A bit of trivia: When I saw "metabole" it made me think of
metabolism. I once put some beans in a bird feeder. They birds would not touch them. I finally learned that there
is a substance in uncooked beans that inhibits an important
digestive enzyme. Somehow the birds know that they cannot
digest the beans.