fall out vs fight like cat and dog

fall out

verb
  • To leave one's place in the current formation of ranks in order to take one's place in a new formation. 

  • To leave one's current location to report for duty at a new location. 

  • To pass out. 

  • To come out of something by falling. 

  • To cease to be on friendly terms. 

noun
  • Synonym of falling out (“rift following a disagreement or quarrel”) 

fight like cat and dog

verb
  • To fight frequently or irreconcilably. 

How often have the words fall out and fight like cat and dog occurred in a corpus of books? (source: Google Ngram Viewer )