Human bodies being made from matter does not imply that a hypothetical soul must also be made of physical matter.
It may not be scientific to propose that souls exist independent of matter (it seems a hard hypothesis to confirm or deny experimentally), but an idea does not need to be experimentally testable to be possible.
It doesn't even need to be that there are "souls," we just need to find a way to explain what Thought is. Saying it's the lights on an MRI aren't good enough - all the MRI tells us is that blood goes to certain parts of the brain during certain thoughts. Just like a radar gun displaying 50MPH isn't the car actually going 50MPH, so too do we need a way to explain what a Thought or Mind actually is.
So far this hasn't happened. If it had, it would be breaking news, because consciousness would be "solved."
It may not be scientific to propose that souls exist independent of matter (it seems a hard hypothesis to confirm or deny experimentally), but an idea does not need to be experimentally testable to be possible.