Data's Day - S4-E11
Continuity mistake: At the end, Picard shows Data a baby born during the crisis. Neither of them touches it, but between shots, the baby's blanket changes positions. First it's almost completely covering his head and face, then it's pulled down and showing much more of him. (00:42:15)
Data's Day - S4-E11
Revealing mistake: When Data and Dr. Crusher are tap dancing on the holodeck, whenever the camera angle changes to a wide shot from above (for the more complex dance moves), it's clear it is not Brent Spiner but a stand-in dancing.
Data's Day - S4-E11
Revealing mistake: When Data asks the replicator for Feline supplement 74 and gives then gives it to Spot, a bug is crawling on the food. Replicators cannot create living organisms. (00:13:15)
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