It is a comic relief.
Capulet calls for a sword, but lady Capulet insists that it is at most a crutch at this point of his life, or that he could make better use of one. Capulet is old and the days of fighting are long behind him, but him and Montague insist on this nonsense of pretending to be at an age of swinging swords on the street.
Capulet even refers to Montague 'flourishing his blade in spite' of him. This shows that Montague is not even taking part in the actual fight either, just waving his sword around as a provocative old man who also cannot fight.