How do you solve a loose-loose situation?

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I'm sure many of you have experienced it before, either way you are always wrong. Whether you defend yourself or not, you are always faced with defeat. What do you do in such a situation? What are the problems you are facing in such a loose-loose situation? I'm faced with this problem usually with my parents or with some of my ignorant friends. What do you think I should do to prevent such a situation, or should I face the problem knowing that I will 'loose' anyway? Thanks for your response! I hope to get a good discussion going since mostly we experience such problems and don't know where to go with them.