That argument relies on the assumption that the new brain cannot have a continuation of the old consciousness. The consciousness itself isn't a magical floating entity but neither is it directly a physical thing, its a series of interactions between chemicals and electricity. If these conditions are directly replicated then the consciousness would seem (from the perspective of the subject) to continue.
Look at it this way. If you were to snap freeze a person so that all brain activity stopped for a year and then unfreeze them would they continue to be the same person?
Now if you were to snap freeze a person so that all brain activity stopped, destroy the brain, and a year later recreate the brain in identical fashion (still frozen) and then unfreeze them would they continue to be the same person?
In the year inbetween for both of them their brain is entirely inactive, looking at the snap shot of when they are frozen and unfrozen the brain is identical in each case. What is the difference between the two?
