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This quote is from a cringey 80s movie, and it means you're so stubborn you'd rather be wrong than admit you're wrong. You’re like a dog with a bone, and that bone is your opinion.
You're wrong, and I'm right, and I'm not even listening to you.
I'm not going to let you win, even if you're technically right.
I'm not changing my mind, even if I'm obviously wrong.