get someone's goat

Annoy or anger someone, as in By teasing me about that article I wrote, he's trying to get my goat, but I won't let him. The origin of this expression is disputed. H.L. Mencken held it came from using a goat as a calming influence in a racehorse's stall and removing it just before the race, thereby making the horse nervous. However, there is no firm evidence for this.
origin. [c. 1900]

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The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company. All rights reserved.