A lot of science teachers think that Dawkins is speaking science when he is actually speaking scientism. The problem is that they accept they idea that the only "science" that is knowable is that contained in the categories explored by the scientific method. That is a dubious proposition. Huge chunks of human experience cannot be dealt with by the scientific method.
This is simply incorrect. Dawkins is speaking science, there is no such thing as scientism. If you want to deride his journalism, do so based on his atheism. He is an atheist that approaches science on that basis. However it does not cause him to misrepresent the science he is communicating.
"The problem is that they accept they idea that the only "science" that is knowable is that contained in the categories explored by the scientific method. That is a dubious proposition.
Science is the scientific method, anything else is something other than science. If you believe otherwise, give an example.
"Huge chunks of human experience cannot be dealt with by the scientific method."
Of course. Science does not pretend to deal with many human experiences.