That isn't exactly what it's doing. It's proposing that there are two ways we evaluate things — deeply examining and rationally analyzing them in depth to identify specific strengths and weaknesses, and using the very fast pattern-matching "feeling" portions of our brains to identify nonspecific problems. These are cognate to "System 1" and "System 2" of Thinking Fast And Slow.
Having established that people evaluate things these two ways, the author then says, "I will demonstrate to both of these ways of thinking that AI fears are bogus."
Having established that people evaluate things these two ways, the author then says, "I will demonstrate to both of these ways of thinking that AI fears are bogus."