at cross-purposes
(idiomatic) Mutually misunderstanding each other's plans, intentions or meanings.
at cross purposes
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