The Handbags Come Out Meaning

(Britain, idiomatic, soccer, rare) A row intensifies; a dispute becomes heated.

Example: 2008, Chris Charles, BBC Sport, 12 May 2008, “Premier League quotes of the season”:
  "I'm ready to take the blame for all the problems of English football, if that is what he wants."
  The handbags come out early doors when Arsenal boss Arsene Wenger responds to Ferguson's dig about the Gunners' foreign contingent.
2014, Oliver Wheaton, Metro, 26 Jul 2014, “Handbags: Israel has dig at Brazil’s 7-1 World Cup defeat after diplomatic row over Gaza bombing”:
  The handbags have come out after a diplomatic argument between Israel and Brazil got, well, very personal.