Continuity mistake: While Tam is talking to Deanna and sits down, he says "You understood... at least a little, how I felt." While saying this, he places his left hand on his right leg. While still saying that same line, it cuts to an angle from beside Deanna and his left hand is suddenly between his legs.
Continuity mistake: To view their orders and mission, Data puts a drive into the Enterprise's computer while standing with Riker and Geordi. Riker is seen standing but leaning casually away from Data on Data's right, and Geordi is standing off to Data's left. It then cuts show the computer screen, and the three men are reflected in it. The reflection shows that Riker is suddenly almost leaning over Data's shoulder, and Geordi has moved to standing behind Data's left shoulder.
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.
Continuity mistake: In the beginning of the episode, right after Data informs Picard that the USS Hood is on an intercept course, closing at high warp, Picard is shown in the back ground looking down at his arm rest. He looks up and turns his head to his right making it center with his body. It then cuts to a close up of Picard and he is looking to his left, and turns his head again to say "That's odd."
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