Descent (1) - S6-E26
Trivia: Stephen Hawking guest stars in this episode, playing himself as a holodeck character (The "Poker with Einstein" program). This came about when he visited Paramount Pictures to promote "A Brief History of Time", and then told the Paramount people that he had always wanted to visit the Enterprise. He not only got to visit, but the writers added this special scene just so professor Hawking could appear on screen in a Star Trek episode. Hawking also reportedly stopped by the warp engine, smiled and said "I'm working on that".
Descent (1) - S6-E26
Trivia: The building used in this episode and in part two (S7 Ep1) is called "House of the Book" Brandeis-Bardin Institute Hebrew Campus, in Simi, California. It was also used in the early seasons of the Mighty Morphin Power Rangers as the Rangers Headquarters.
Descent (1) - S6-E26
Trivia: Admiral Nechayev tells Picard that the Starship Gorkon will be her flagship. In Star Trek VI: The Undiscovered Country, the Chancellor of the High Klingon Council was named Gorkon.
Answer: He brought the Borg to the Alpha Quadrant and showed them that it was full of worlds waiting to be assimilated. Guinan's homeworld was their first stop, and they assimilated everyone and took over the planet, leaving The Survivors of her race without a home. Q is ultimately responsible for that.
Captain Defenestrator
By the time Q takes the Enterprise to meet the Borg, Guinan already knew who they were and they had already destroyed her world. Therefore the above answer can not be right. I believe Guinan is much more than she appears, and her people have had encounters with the Q in the past. It is these interactions, that obviously were not pleasant, that fuels her distrust.
oldbaldyone
That's what the above answer is saying. Q brought the Borg to the Alpha Quadrant (not Earth) and the Borg destroyed Guinan's home world in the late 2200's, which is why she hates Q. Although she met Q in 2160 and they both saw each other as enemies right away.
Bishop73