What is wrong with the following 'proof' that all cupcakes have the same flavor?

What is wrong with the following ‘proof’ that all cupcakes have the same flavor?

“Suppose there are n cupcakes in the world. We induct on n. If n = 1 the result is clear (since any cupcake has the same flavor as itself).Fix a positive integer n > 1 and inductively assume that any collection of n − 1 cupcakes has the same flavor. We show that all n of the cup cakes in the world have the same flavor. To do this, place the cupcakes in a line and label them c1, c2, . . . , cn. By the inductive hypothesis, the first n − 1 cup cakes c1, c2, . . . , cn−1 and the last n − 1 cupcakes c2, c3, . . . , cn all have the same flavor. In particular, the cupcake c1 has the same flavor as the middle cupcakes c2, c3, . . . , cn−1. Also, the cupcake cn has the same flavor as the middle cupcakes c2, c3, . . . , cn−1. We conclude that all of the cup cakes c1, c2, . . . , cn−1, cn have the same flavor, as desired.”