Continuity mistake: When young Picard sees his "father" Riker, he says to turn on the computer in schoolroom 8. In the scene showing the children gaining access to the computer, the terminal they are at shows classroom 7 across the header of the screen. (00:36:20 - 00:39:55)
Other mistake: When Ro Laren enters the Jeffries tube, she makes a sudden shift to her right (our left) as she begins crawling; she was trying to avoid the camera.
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