"Could you tell us something that you're proud of about Mexico for?"
Why is 'for' added in this sentence?

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I wouldn't add 'for' to that sentence. In your sentence, 'about' and 'for' are fulfilling the same purpose. I would say either of these:
"could you tell us something that you're proud of about Mexico?"
"could you tell us something that you're proud of Mexico for?" (<--- this sentence is not as grammatically correct as: could you tell us something about Mexico for which you are proud?, but most native speakers won't phrase the sentence like that. You might only come across it in a book/novel).