dichotomy

dichotomy    [dahy-Kot-uh-mee]

noun.  a classification into two opposed parts or subclasses

"The dichotomy between eastern and western culture."

"All cars are either small and efficient or large and polluting creates a false dichotomy because there are some cars that don't fit into either category."

"The role of mother or not-mother is such a deep dichotomy for women in our culture."