The argument does not need to involve typical human behaviour with its faults. Because if a computer can simulate humans, it can also simulate humans with error correction and verification mechanisms. So, the computer should also be able to simulate a process where a group of humans write down initial deductions and then verify it extensively for logical errors using both computers and other humans.

Most of the objections have been covered in his book "Shadows of the Mind".

Also, the fact that most human behaviour is not about deducing theorems isn't relevant as that is used as a counterexample which attacks the 'computers can simulate humans' hypothesis. This particular behaviour is chosen, as it is easy to make reflective arguments precise.