how to understand the “withdrawn behind the untouchable screen of his white coat.”？
In the end she went with plain old, 'Thank you, doctor," but he'd already withdrawn behind the untouchable screen of his white coat.

Question

Answer

The writer is saying that the doctor is being cold and impersonal, he is using his role as a doctor (white coat) to be detached (untouchable)  from personal contact (the screen is against treating her as a person),