To argue in your dream reflects your internal struggle with your own conflicting needs and belief systems. You are grappling with your inner polarities and paradoxes, attempting integration and synergy. See Integration Dreams.
If you are arguing with someone, it shows you are set in your opinion about what that person represents to you. You are now willing to stick up for yourself in that matter and stick to your guns, so to speak, about it. You will need to re-evaluate the matter to see if this is something you are doing that is in harmony or out of harmony with your being and world.