It means that whoever you were speaking to was able to embarrass you or prove you wrong in an assertion you made upon a subject, especially with an audience. To 'get one's goat' means that someone is speaking on a subject professing untruths and/or embellishing the truth in front of an audience while someone in the background steals the speaker's goat from his herd while the owner has captivated the other's attention.
"Gets my goat" means annoys and irritates me.
To "get someone's goat" means to annoy or irritate them. The origin of the phrase is unclear, but it likely comes from the idea of stealing a goat, which was believed to be a calming influence on horses when placed nearby.
A goat will eat almost anything according to "common knowledge." If you leave a goat in charge of your garden, it may eat all of your plants and you may get no food from the garden. A related idiom is "Letting the fox watch the henhouse."
Hedge can have both of these meanings.Though the usual idiom is 'don't hedge me in', 'don't hedge me' is also possible.
to go all out to get someone angry.
It is not an idiom, it means your nose is itching.
It's not really an idiom. It means "what are you thinking about."
RFP is not an idiom. It's an abbreviation.
A polled goat is hornless.
"Sieve" is not an idiom. See the related link.
It's not an idiom. It means the tip of your nostril.
idiom means expression like a page in a book