Why does she say “close”? What did he want to do?
She said "close" because she thought the dog was supposed to roll over when the dad went "bang!" Instead, the dog pawed at the "gun" the dad made with his hand. That is why he clarifies "No, I taught her to go for the gun." The dad is telling Claire that he did not train his dog to roll over when he goes "bang", but to paw at the gun he makes with his hand.
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