Does this argument refuting the existence of superintelligence work? A superintelligence is a machine that can surpass all intellectual activities by any human, and such a machine is often portrayed in science fiction as a machine that brings mankind to an end.

Any machine is executed using an algorithm. By the Church-Turing thesis, any algorithm that can be executed by a modern computer can be executed by a Turing Machine. However, a human can easily simulate a Turing Machine. Doesn't this mean that a machine can't surpass all intellectual activities, since we can also execute the algorithm?

This argument is most likely flawed, since my intuition tells me that superintelligence is possible. However, it is not clear to me where the flaw is. Note that this is my own argument.
I believe this argument is based on the fact that intelligence is a single dimension when it really isn't. Are machines and humans really on the same level if a machine can solve a complex problem in a millionth of the time a human can? 

It also assumes that the Turing machine is still the best computational model for the time period that you are in, which is not necessarily true for the future, it is just true until this point in time.