Find the flaw in the following proof: Theorem: All horses are of the same color.

Question

Find the flaw in the following proof:
Theorem: All horses are of the same color.
Proof: Let there be n horses. We proceed by induction on n. If n = 1, there is nothing to prove. So assume that n > 1 and that the theorem holds for any group of n - 1 horses. From the given n horses discard one, say the first one. Then all the remaining n - 1 horses are of the same color by the induction hypothesis. Now put the first horse back and discard another, say the last one. Then the first n - 1 horses have the same color again by the induction hypothesis. So all the n horses must have the same color as the ones that were not discarded either time.

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