The "appropriate
sex" is a phrase helpful in these sexually
enlightened times when a
person's preferred
sexual partner is admitted to not necessarily be of the
opposite sex. For example: to a
homosexual, a "member of the appropriate sex" refers to a
member of the same sex; to a
bisexual, it can refer to either
male or
female; and to a
heterosexual, it refers to a
member of the opposite sex. In a pinch it can even cover the
transgendered. So really, it's a much more accurate term to use than "the
opposite sex".
Cletus the Foetus has pointed out that an even more appropriate phrase would be "the preferred sex", as even "the appropriate sex" is somewhat normative.