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He plans to drown it because the dog might give away his identity if it has been described.
"The dog, though. If any description of him were out, it would not be forgotten that the dog was missing, and had probably gone with him. This might lead to his apprehension as he passed along the streets. He resolved to drown him, and walked on, looking about for a pond: picking up a heavy stone and tying it to his handerkerchief as he went."
Oliver Twist/ Chapter 48