They are filing for divorce, citing 'irreconcilable differences'. [=they cannot agree on most things or on important things]
theories that are 'irreconcilable' with each other
(..) but the truth, so help you God? SCARLET: I do. You request a divorce by the state of California... ...citing irreconcilable differences. This correct? - Yes, Your Honor. - Is Michael O'Donnell present? No, Your Honor. I take his absence as agreement (..)2009 17 Again