Devil's Due - S4-E13
Continuity mistake: As the camera does a close up on the shuttle craft's forward window as it approaches the Enterprise, the dorsal section is seen getting larger the closer they get. As Data and Picard talk, the image fades out, and a minute later, the angle changes, the dorsal section is again seen getting bigger, and the ship disappears.
Devil's Due - S4-E13
Continuity mistake: In Picard's quarters, Ardra appears as Troi. After reappearing as herself, she puts her hands on her hips. After the angle change, she repeats the motion.
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