Here is a snippet where phrase came from:
"We never argued you into taking over the management of those
boats. We argued me into it. I'm the goat. You have nothing to do with it. You retired ten years ago."

What is the meaning of the sentence: "I'm the goat"?
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person who takes blame for another's action
Right. He is taking the heat for having made the decision to buy the boats just when the bottom fell out of the business.
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An acronym....Greatest.Of.All.Time.....G.O.A.T.

"I'm the goat" means the one who falls into what is thrown out on the topic. Jokes and work topics are the most common. Some are for fun and some are serious. It’s best to be aware on how you throw this catchphrase.