You are in very dangerous territory if one day you happened to find yourself contemplating genocide because you thought you had a good excuse for it. Inevitably something unplanned happens. A deadlier threat emerges, or everybody gets killed anyway but in different circumstances, or you become so corrupt that people try to kill you.
Compare the Borg to all other great Federation enemies.
They are not like the Klingons. The Borg don't believe in honour, and cannot be reasoned with if you show yourselves to be honourable.
they are not like the Romulans. You can't sign a treaty with them, and let them hide behind the Neutral Zone.
They aren't like the Cardassians. The Cardassian border war only ended since it was a stalemate, and continuing the fighting made no sense to either party. Stalemate between the Borg and the Federation is like a boxing match between Mike Tyson in his prime and a ninety year old man. no contest.
They aren't like the Dominion. Even though the Founders of the Dominion detest all solids everywhere, they (for now) are willing to retreat to the Gamma Quadrant and stay out of the Alpha Quadrant's business. I say for now since I think one day they'll be back, but i'm digressing.
Since the Borg are far superior technologically to the Federation, will not relent until they assimilate the Federation, and never understand the concept of co-existence or peace, then I can certainly understand Picard's reasoning at the start. In a sense it's a "them or us" scenario.
Of course, there is the moral aspect of the argument, which has a strong case. But let's pose a hypothetical scenario. say in Best of Both Worlds, the Enterprise-D under Riker as a last resort warped into the Borg Cube (as they nearly did) and destroyed most of it. However, Locutus and some other Borg survived and beamed down to Earth, and started to assimilate humans on the planet. Would it be bad to infect the Borg with a virus then?
What if they assimilate Earth, and then moved from one Federation member world to the next? What if they attacked Qo'nos, Romulus, Cardassia or Ferenginar? They could easily have done this, since to the Borg the Klingons, Romulans, Cardassians and Ferengi would all be good candidates for assimilation. In the good of the Alpha Quadrant, why not act?