> This presumes that playing into their hands would actually bring forth enough support to rebuff the reaction. If forces overwhelmingly squash the terrorist organization, then it doesn't matter if it plays into said organization's hands.
That is true as far as it goes, but the fundamental problem is not IS, nor Al-Qaeda, nor any single terrorist group out there, nor even all terrorist groups taken together. It's the extremist ideology that appeals to young, angry men across the Muslim world. Taking out Al-Qaeda in 2001 didn't have any effect in the long term. Going to war with Iraq in 2003 actively made the problem worse. Killing bin Laden in 2011 didn't really do anything one way or the other. If the West goes in now, and (figuratively) nukes Syria, then why would we think that will solve the problem, when it never has before?
If you want to win this like you win a war, by killing your way to victory, then you have to kill not just everyone who's currently carrying a gun, but everyone who may pick up a gun as a reaction to that killing, and everyone who may pick one up as a reaction to killing them, and so forth. That kind of total war is immoral, in my view.
Our approach to defusing this threat should not be focused on killing individuals, but on removing the motivations they have for fighting us in the first place, without judging whether, in our view, they are valid or not. The fact that they have them, right or wrong, is all that matters. I don't know what will achieve that, but after responding to over 30 years of Islamic violence with force and force alone, and failing to really have much impact, we should recognize that a change in strategy is required.