The non-materialist argument is similar to creationist critiques of evolution. Scientists who study these things see a material explanation, but because these are enormously complex emergent properties they don't know the exact details. Critics then use a god of the gaps argument, saying that if a material explanation can't explain everything right now then a supernatural explanation (which which explains far less and runs counter to available evidence) should be favored. Behind both arguments lie an unease that the scientific approach knocks humans off their pedestal and makes them seem like everything else.

It's not surprising that the only neuroscientist in the article is arguing for a materialist approach.