cross-purpose

n.	1.	A counter or opposing purpose; a contrary aim; hence, that which is inconsistent or contradictory.
	2.	A conversational game, in which questions and answers are made so as to involve ludicrous combinations of ideas. To be at cross-purposes to misunderstand or to act counter to one another without intending it; - said of persons.

Noun

1.

cross-purpose - a contrary aim; "at cross-purposes"

aim, design, intent, intention, purpose