The ability to reason with a stranger in a dream may indicate that you believe other people interfere with your happiness in real life. After all, the purpose of an argument is to comprehend the viewpoint of another person.
If you have a heated argument with a stranger, it may indicate that you need to try to understand other people's points of view and discuss "issues" with those with whom you may disagree.
If the stranger appears unusually or strangely during the dream, it is possible that your subconscious mind is arguing with you.