The Unicorn Tapestry

This novella is also available in Nebula Award Stories Sixteen (1983), and was originally published in New Dimensions II (1980).

From the novel The Vampire Tapestry.

Dr. Floria Landauer's newest patient, Edward Weyland, suffers from the delusion that he's a vampire, not the undead variety but a predator that's co-evolved with humans to drink their blood. This idea has threatened his career as an anthropologist, and he needs a bill of good health to resume his position. However, as Weyland describes his "fantasy," Floria suspects she's being handed the truth dressed up as a lie, and the therapy becomes a fascinating contest of wills where trust and respect vie with mortal imperatives.