Revealing mistake: In the shot where Geordie walks into the bridge of his mother's ship and finds that everyone is dead, if you look closely at the bottom right of the screen as Geordie is walking into the bridge you can see that one of the containers on the ground is quickly moved into place by a woman who is dead. (00:13:40)
Revealing mistake: The 'dead' woman moves the barrel towards herself. (00:13:40)
Revealing mistake: When Data gives Spot his food, when he puts the food on the ground you can see his normal skin (human skin). (00:16:35)
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