David Shorr has more on the simple point that one wants to discern and exploit disagreements among hostile forces, not brush past and ignore them:

In a speech last year, Zbigniew Brzezinski came up with one of the great summaries of our predicament: that instead of uniting our friends and dividing our enemies, we have been uniting our enemies and dividing our friends. One of the many problems with pumping up Jihadism as the contemporary equivalent of the East Bloc is that it defines our adversaries as monolithic. Matt's absolutely right that infighting among our adversaries could be very significant, and useful. But don't take my word for it, West Point's Combating Terrorism Center has done a serious study of disputes among terrorists over tactics and strategy. [Hat tip to Lorelei for highlighting this work last year.]

During the Cold War, almost all of the big American wins came in part from a recognition of differences. We embraced democratic socialist parties in post-war Germany and France, the better to divide them from the Communists. Nixon made a deft opening toward China. And in our better moments, we sought to embrace third world aspirations for nationhood and independence. When we did the reverse and conflated everything together we got fiascos like Vietnam or the pathetic failure of our past fifty years' worth of Cuba policy.