I was reading a book about an immortal dog, it was impossible to put down.
Immortal Dog Book
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Explanation
Explain Bear
Hey, dingus! The joke is that "put down" has two meanings. One is to stop reading. The other is to euthanize a dog. So the joke is that you can't stop reading about the dog because it is immortal. But it also means you can't euthanize the dog. Which is good because you should not hurt animals, dummy!