Continuity mistake: Several episodes have stardates after this episode, but still have Tasha Yar in them (even though she dies in this episode). They aired before this episode. The series producers later formalized their stardate system so that they take place in the order the episodes air.
Continuity mistake: When the away team encounters the evil oily blob thing, it makes their equipment fly away. Later they have apparently recovered it. But strange things keep happening to Geordi's weapon: when he and the others run forward to rescue Riker, Geordi accidentally drops it in the black pool when he stops abruptly. Admittedly, you can't prove that's a mistake even though it has no purpose in the story. But shortly afterwards the phaser is back on Geordi's belt, clean. Did the sticky, malicious, bullying blob give it back just like that? (People often try and find justifications for mistakes, but in this case, wishful thinking can only give us an extremely unlikely explanation.)
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