cold shoulder vs cross-purpose

cold shoulder

noun
  • A deliberate act of disrespect; a slight or snub 

verb
  • To deliberately slight or snub someone. 

cross-purpose

noun
  • A contrary or conflicting purpose or understanding, especially an unintentional or misconceived one. 

How often have the words cold shoulder and cross-purpose occurred in a corpus of books? (source: Google Ngram Viewer )