enantio- stems from a Greek root meaning opposite or against and -dromic from a Greek word for course or racecourse; thus, against the (normal) course, and by extenstion characteristic of something that has become its opposite.

Julian Burnside has an interesting essay which expands on enantiodromic words:
http://www.users.bigpond.com/burnside/contradicting.htm

http://wordsmith.org/board/showflat.pl?Cat=&Board=words&Number=451