been years since I seen it, but I don't remember that being Q's motive.
didn't Picard say something that made him mad and then he fingersnapped the Enterprise to the other side of the universe?
again, haven't watched in a long time
but if memory serves me correctly, didn't they admit on that episode that if Q hadn't did what he did, then the Borg never even would have been aware of the Federation for a very long time?
I thought the whole gist was that Q forced the Federation into a conflict that they hadn't evolved to be ready for yet. If the Borg didn't show up for another 1000 years, then chances are that the Federation would have had some new technology and they would have been able to handle them efficiently
as opposed to taking somebody from 1746 with a musket gun and dropping them off in 2018 Syria
so again, it was Q's fault that whole thing happened.