It also caught on because, while he never said it in the original books and short stories, it’s something he absolutely could have said. He described things as “elementary” and used the phrase “my dear Watson” more than once, just never in quite that order.
For instance, here’s a bit from The Crooked Man:
“I have the advantage of knowing your habits, my dear Watson,” said he. “When your round is a short one you walk, and when it is a long one you use a hansom. As I perceive that your boots, although used, are by no means dirty, I cannot doubt that you are at present busy enough to justify the hansom.”
“Excellent!” I cried.
“Elementary,” said he.
It’s just a coincidence that he never used the two phrases in one sentence.
I think it caught on because few people have read the books. Once they used it in media and continued to that is what folks know of sherlock holmes.
It also caught on because, while he never said it in the original books and short stories, it’s something he absolutely could have said. He described things as “elementary” and used the phrase “my dear Watson” more than once, just never in quite that order.
For instance, here’s a bit from The Crooked Man:
It’s just a coincidence that he never used the two phrases in one sentence.