Argue dream meaning is explained below using 3 different sources. Each interpretation is shown with its source.

Interpretation 1 — Silvana Amar

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. 
Source: The Bedside Dream Dictionary Author: Silvana Amar

Interpretation 2 — Dream Explanations - Anonymous

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.

Source: Strangest Dream Explanations Author: Dream Explanations - Anonymous

Interpretation 3 — Stearn Robinson - Tom Corbett

This is a lucky dream of contrary unless you lost your temper, in which case it is a warning against making impulsive decisions in important matters.

Think carefully before you act

Source: The Complete Guide to Interpreting Your Dreams Author: Stearn Robinson - Tom Corbett