That moment is nonsense. Why would the Q give a rats ass about provoking the Borg?
They probably just shoved that into the episode to make the Borg seem even more menacing and mysterious.
Though you could probably come up with all sorts of reasons; for instance if we assume the Q shepherd certain species (like humanity) towards ascension into something like themselves then Q might have just jeopardized one of those species (humanity) and maybe blinking the Borg out of existence or helping humanity against them would be prohibited by their form of the prime directive.
Or if they are interested in maintaining some sort of "balance" between the major powers of the Milky Way then the Borg taking over the Federation would ruin that.
Or something like that.
Imho, the bigger problem with that whole scene is really Q's reaction to Guinan and how that never went anywhere.
It also highlights one of the big problems I have with the whole Q nonsense.
Like...how did the Borg pass their trial? Or the Klingons? Or the Kazon? Or the Founders? Or the Cardassians? Or the Vaadwaur? Etc. Etc. Etc.