I've come across this argument before. I think Ravi Zacharias makes a big deal out of it. He says the mind cannot come about from a material source as if that is a sacred law that you cannot disagree with. I don't see why not.
These people together with the woomeister Deepak Chopra treat the mind as if it were some magical thing. But the mind is nothing more than the product of the brain which is material. To say that the mind is independent of the brain, one must show evidence that the mind can survive the brain. If you can't show such evidence, it's pure speculation.
Ultimately, I wish my fellow Christians won't prolong our agony. We haven't got the smallest logical leg to stand on. Sometimes, it's our pride and ego that prevent us from admitting this. We feel foolish when atheists tell us our faith is illogical. But if we truly believe that it's Christ who must increase and we decrease, we won't have this horrible pride and ego any more. Then atheists will find it easier to talk to us because we won't have this obstinate refusal to admit our faith is illogical when it so obviously is. It is wisdom to capitulate when we clearly have no ground to fight. Otherwise, atheists will rightly think we are idiots who can't understand their rational arguments. The fact is we can see they are logical but our egos won't let us admit that.
Cheers,
St Truth