The dermatologist was fired

This joke delivers its chuckle with a clever bit of wordplay, specifically a pun that hinges on a double meaning. The key is the word "rash." In the world of dermatology, a rash is a common skin condition, something a skin doctor would encounter daily. But "rash" also describes something done hastily or without careful consideration – a "rash decision," if you will.

The humor then springs from the unexpected collision of these two meanings. We expect the dermatologist's firing to be related to their professional competency with skin ailments, but instead, it's attributed to poor judgment, using a term that just happens to be a staple of their medical field. It’s a delightful linguistic twist, taking a common idiom and twisting it back into the professional context of the person involved, proving that sometimes, even doctors can be victims of their own specialized vocabulary.