(of two people) be continually arguing with one another.
1995 - Edward Toman - Dancing in Limbo - Her desertion of him hadn't come as a total surprise... for the pair of them had been fighting like cat and dog for the best part of a year.
RELATED IDIOMS :
fight fire with fire :
use the weapons or tactics of your enemy or opponent even if you find them distasteful
1998 - New Scientist - Many opponents of biotechnology might say that they are simply fighting fire with fire. After all, the biotechnology industry is not averse to misquoting people when it suits them.
fight a losing battle :
be fated to fail in your efforts
fight or flight :
the instinctive physiological response to a threatening situation which readies you either to resist violently or to run away
fight shy of :
be unwilling to undertake or become involved with
1992 - Farmers Guardian - Welsh companies often fight shy of dealing with the big multiples.