The problem occurs in the induction step going from n=1 to n=2. Removing one cow from a field of one cow leaves an empty field. Hence when the new cow is added, there is no cow to compare its colour to. Putting back the first cow we thought of leaves us with a field of two cows, but they are not necessarily the same colour.

This is probably the point to conclude that the Theorem was bull, but then we wouldn't want to milk the problem (groan).