Arguing in a dream often surfaces a tension that hasn't found its way into a real conversation yet -- feelings you've suppressed rather than voiced, playing out where it feels safer to let them show. The person you're arguing with may simply be standing in for whatever the actual disagreement is really about.
It is much worse for an Artist to conceive he knows those things which he is ignorant of, than to be ignorant of those thing which he ought to know. - Cardan Girolamo (1501-1576)