Revealing mistake: Just after Riker and Geordi are talking in the turbo lift, it cuts to a view from outside the ship and shows the USS Hood flying next to the USS Enterprise. As the ships draw nearer, the views of both ships overlap, and a black mat outline can be seen around the saucer section of the Hood as it passes by the Enterprise's starboard nacelle.
The Best of Both Worlds (2) - S4-E1
Factual error: Shelby announces the Borg have entered Sector 001, and we get an exterior shot of the Borg ship flying past Saturn. The problem is that the Borg are approaching from the side of the planet illuminated by the sun, meaning they would actually be moving AWAY from Earth rather than toward it.
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