When do doctors get angry?
Why this joke works
An Empty Waiting Room Sounds Like Lost Calm
Running out of patience means becoming unable to stay calm about a delay or annoyance. “Patients,” the people a doctor treats, sounds very similar to “patience.” The question’s reference to anger primes the emotional meaning, while the occupation makes the medical spelling fit. The answer can therefore suggest both a doctor becoming impatient and a practice with nobody left to see. This is a vocabulary collision, rather than a claim about how real doctors behave.
A closer look
A Plural Noun Replaces Something You Cannot Count
Patients can be counted individually; patience is normally treated as an amount of a quality. “Run out of” happens to work with both. That shared phrase lets the substitution pass through the sentence without changing its grammar. The written punchline makes the countable version explicit, while someone hearing it may briefly imagine the ordinary expression before noticing the profession-specific meaning.
Fact behind the joke
Both Uses of “Patient” Have an Old Connection
Merriam-Webster traces both the adjective “patient” and the medical noun to Latin pati, meaning to suffer. It records English uses of both in the fourteenth century. The calm person and the person receiving care are therefore not connected only by a modern coincidence of spelling; the two uses share a much older linguistic background.