Noun
cross-purposes
plural of cross-purpose
cross-purposes (uncountable)
(dated) A conversational game, in which questions and answers are made so as to involve ludicrous combinations of ideas.
But these programs often work at cross-purposes with federal price-support incentives to produce corn and other commodities. Source: Internet
Empathy then, becomes unnecessary, and/or at cross-purposes to their needs. Source: Internet
I’m not claiming that the two goals are working at cross-purposes. Source: Internet