This often indicates there is a major problem in your waking life and it may require a new strategy in dealing with it.
Fighting also points to war, which involves strategy. Dreams about fighting often highlight that it is time to employ a new strategy with the situation you are dealing with.
Dreaming about fighting is often a sign of emotional turmoil of some sort, and this is the case whether you are arguing with others in your dream or not.
Dreaming About Fighting With Someone You Know
Dreaming About Seeing Others Fighting
Dreaming About Fighting With Intense Feelings of Anger
If you are feeling particularly angry in your dream while fighting, it indicates that you are stifling your emotions in real life.
Society does not approve of negative emotions and people often have to hide them. It is only natural that they should appear during our dreams, as the negative emotion gets filtered into our subconscious and eventually needs an outlet.
This outlet then appears in the form of dreams and can be distressing for the individual. The message from the subconscious here is to find a healthy way to deal with negative emotions during waking life so that it does not feel compelled to release them during sleeping life. Meditation, yoga, exercise, and creative projects can be excellent ways to release intense emotions while you are awake.
Learn more about Dream Interpretation here.