Where does the phrase "got my goat" come from?

This phrase may or may not have anything to do with horses. To "get one's goat" is to make one
angry or mad, and it more likely came from a naval tradition of keeping ship's goats.

However, there's another popular etymology which, while it has no evidence, makes some sense.

In order to reduce stress, racehorses that travel a lot often have companions that go with them. A variety of animals are used - miniature horses, donkeys, chickens, etc. Goats, however, are one of the most common. Goats and horses get on well together - in some parts of Europe co-grazing goats with horses is done for pasture management.

Stealing a racehorse's companion would make the horse antsy, stressed, and even angry - and thus unlikely to perform well on race day.

There's no actual proof this has anything to do with the saying, but it's a cute idea.