When you are arguing in a dream, it is the brain prepping you for verbal confrontation. The person you are yelling at represents all the negative aura in your waking hours and you need to get rid it by telling him or her to quit bothering you.
Arguing also provides a release point for pent up emotions and energies. The more you exert your vocals and logic reasoning to win an argument, the more you will feel in your element whatever the challenge.