Guinan: I hear they drummed you out of the Continuum.
Q: I like to think of it as a significant career change.
Guinan: Just 'one of the boys', eh?
Q: One of the boys with an I.Q. of two thousand and five.
Data: The Captain, and many of the crew, are not yet convinced he is truly human.
Guinan: Really? [Picks up a fork and stabs Q's hand.]
Q: AAARGH!
Guinan: Seems human enough to me.
Star Trek: The Next Generation (1987)
2 quotes from Deja Q
The Royale - S2-E12
Factual error: 30 seconds in Geordi says: 'surface temperature -291 degrees Celsius'. (The scale only goes down to -273.15 which is absolute zero). (00:00:30)
Trivia: Another joke from the set designers: whenever someone is in the Jeffries Tubes, you will see several pipes on the walls labeled "GNDN" this stands for "Goes Nowhere, Does Nothing."
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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