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A person convinced against his will is of the same opinion still - Dale Carnegie
At its core, this quote means that forced agreement is meaningless. If you strong-arm someone into saying "you're right," you haven't actually changed their mind; you've just silenced them.

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If you argue and win, you lose. Because you made the other person feel inferior - Dale Carnegie
The core message is that a tactical victory in an argument often leads to a strategic defeat in the relationship. You might be right, but you end up making an enemy.

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You cannot win an argument. You can only avoid it - Dale Carnegie
The core message is that in human relationships, a tactical victory in a debate is often a strategic defeat. You might prove your point, but you'll likely alienate the other person in the process.