It is the simple tale of an innocent psychiatrist who inadvertently, and unfortunately "catches" his patient's insanity.
I've seen that actually be a sort of "running joke" in an ongoing CoC game. It was a near-future CoC game with the investigators being part of a major metropolitan police department, investigating an increase in cult-related crimes.
The PCs would see horrible things, which would take a toll on their sanity. They would speak with the department psychiatrist for counseling regarding what they saw. The NPC therapist could make treatment checks to improve their sanity, but at the same time he would hear these unspeakable horrors, which cost him his own sanity.
Every so many sessions, the department psychiatrist would resign and they'd have a replacement.
Speaking of psychiatrists, and continuing on with my earlier Terminator analogy, Dr. Silberman is another good example of losing sanity.
At first he's 100% convinced that Kyle is insane, a violent crazy person with strange delusions about human-looking monsters from another time. Years later, he's working at a mental hospital, now treating Sarah since she seems to have developed Kyle's identical delusions. He knows Sarah is violently, dangerously insane. He's seen what she's willing to do because of her delusions.
Then, Sarah escapes from the mental hospital, as he witnesses what looks like a police officer just melts through a barred door, then takes multiple direct gunshots at close range (leaving strange, silvery wounds) while running inhumanly fast. He is left stunned by the experience.
Then, depending on which continuity you go with, he's lost a lot of sanity.
In Terminator 3: He's working as a grief counselor for the City of Los Angeles. He tries to counsel Katherine, but from his own words he's obviously hiding his own mental trauma, the moment he sees that face again, he is struck with horror and runs blindly into the distance.
In Sarah Connor Chronicles: He's resigned from his job and is living in a house in the woods. When an FBI Agent investigating the strange happenings he was tied to comes to knock on his door, he ambushes the agent and holds him prisoner, convinced that he must be one of those monsters from another time, come to finish him off as a witness.
Also, Miles Dyson is an example of losing sanity VERY fast. We see him late one afternoon as a devoted family man, two kids and a wife, nice big house, clearly a successful and happy man. Later that night, after being shown some impossible things, and being told what the explanation for those things is he's willing to quit his job and end his career. Then he's willing to destroy his workplace utterly and blow it up. He actually is willing do essentially suicide bomb his employer because of the impossible things he'd seen and heard.
The whole Terminator analogy is good to show that sanity loss in CoC isn't just spontaneously developing mental illnesses because you see a monster (although the raw shock of it is a little part of it), it's more the idea that you've learned horrible truths about the world and that now you see everyone and everything in a completely different way and acts that "normal" people would call crazy now make sense to you, and if you try to explain why you are doing everything you will sound completely mad.