Makes you mad. Elicits an emotional rather than logical response. Annoys severely.
This expression, while known to most Americans and used since the early 1900s, does not have its beginnings documented. According to H.L. Mencken in American Language (1945), the saying probably originated around horse racing tracks. He was told that there was a practice among some horse trainers of quieting a particularly high-strung horse by putting a goat in its stall. Opponents would “Get One’s Goat” by taking it from the stall, causing the horse to become unsettled and lose the race.
Join the International Goatkeepers Society
The International Goatkeepers Society is a fun and effective self-control tool for children and adults. Available as individual keepsake pewter gifts and herd sets of 10 for “kids.”
"Get Your Goat" - The Expression
Somebody's got my goat
He must have gone a-strollin'
Though he was old enough to vote
He's lost, strayed or stollen
When he began to feel his oats
He went out chasing nanny goats
You never struck such a giddy old buck
Has anybody seen my goat?
(words by Edward Madden, music by Theodore Morse.  F. B. Haviland pub. Co., New York, N. Y. C 182830, June 3, 1908.)