In theory, to prevent Congress from ever taxing income again.
The reality is it's a red herring put forward by opponents of the Fair Tax to ensure that nothing is done. If you insist that the 16th be repealed first, then Congress has to pass it, and send it on to the states for 2/3 of the legislatures to pass. Then they can say their hands are tied until the states pass it, which probably won't happen. The income tax can be repealed like any other legislation. Then if someone wants to bring it back, they need to start from scratch, passed in both houses, over a fillibuster in the Senate, and signed by a president. And this would have to happen with all the public outrage that would occur once people were used to never having to file a tax return again.