Why does martin luther king use chiasmus in his letter from birmingham jail?

King and his supporters had been labeled as extremists. By using chiasmus ("So the question is not whether we will be extremists, but what kind of extremists we will be"), King manages to turn the attack upside down, appropriating the term instead of rejecting it. His point is that there is nothing wrong with being an extremist for love. Jesus was also such an extremist.

By the way, chiasmus is a figure of speech in which two clauses are presented in their regular order, and then reversed. 

Americans agreed to the settlement terms established by the mexican government.