"What Have I Done?", a short story by Mark Clifton, from Astounding Science Fiction, May 1952, available at the Internet Archive. Here is a quotation from the story:
There are others who can match my record in taking case histories. I happened to be the one who came in contact with this fellow. For thirty years I have been listening to, talking with, counseling people—over two hundred thousand of them. They have not been routine interviews. I have brought intelligence, sensitivity and concern to each of them.
Here is a review from Omphalos:
An industrial psychologist prides himself on being able to instantly categorize any person that he meets. In a drugstore one day he encountered a man who had no outward show of emotion, and was thus uncategorizable to him. Intrigued by the possibility of finding a new type of personality he pursued the man and lost him, only to find later that the odd man reported to the psychologist's job agency in search of employment. Excited still by the prospects, the psychologist sat down to interview the man. It soon became apparent to the psychologist that this man was more different than he had originally thought. The psychologist was a SF fan, and had a very open mind. He thought that the man, named Hoffman, was an alien pretending to be a human. It did not help Hoffman that he kept referring to the ten planets of the Solar System.
Still intrigued the psychologist followed Hoffman to a house in the suburbs. Confronted with questions, the owner of the house, an old woman, denied any knowledge of Hoffman. A few months later a Norwegian named Johnson showed up at the employment agency who demonstrated the same curious lack of affectation and emotion. The psychologist pegged him as the same man right away, and Johnson admitted that he was indeed an alien. He was from Arcturus and he was there with thirty other of his species, disguised as humans. They were there to colonize Earth, but they had not decided on how to do it yet. One option was to wipe the face of the Earth clean of humans and start reproducing. The other option, the one they favored as more humane, was to integrate into the human population and mate among themselves while denying humans the right to mate and reproduce, and delude the humans into thinking nothing was wrong until they were gone for good. The aliens were impressed with the psychologist's powers of observation, and wanted to recruit him to teach them how to integrate. If he denied them assistance, then they threatened to just wipe all life on Earth out and start over.