During the day we can meet people that challenge us through a type of conflict. It is usually not the easy relationships in our lives that keep us growing, but the challenging ones. In the same way, characters that challenge you in a dream are attempting to bring something new into awareness. The particular character challenging you can represent a side of you that is undergoing exploration. Explore an adjective you would use to describe the person you are quarreling with in a dream. How does the character portray an aspect that you may be discarding, adopting or perhaps ignoring? The quarrel brings this issue forward for your consideration. See People, Attack and Being Chased and also Shadow and Archetypes and Universal Characters.