Quote Originally Posted by Stratiotes
Why is it, do you think, we have not done very well at exploiting their internal divisions and squabbles? Is it that we have not acknowledged they exist like the article implies or is it something else?
I don't believe the article implies that we "don't acknowledge they exist", rather it attempts to describe how little policy-makers and pundits tend to really understand the internal divisions within and among the various elements of Islam.

But as far as exploiting such divisions goes, if you read to the end of the article you saw:

...woe betide any western strategist who thinks the problems of the Muslim world can be addressed by a policy of “divide and rule”. The most likely result of that is that western countries will be blamed for divisions that have already existed, in one form or another, since the founding of Islam.

We don't do very well at leveraging the particular characteristics of any one group of Muslims in the direction of our policy goals because it requires too great a subtlety in action. Can you imagine a national level policy based upon in-depth understanding of the specific fusion of religious belief, cultural upbringing and socio-economic factors that drives the manner in which a multitude of factions participates in politics and or violence? A policy geared, not towards setting one faction against another, but towards developing real cooperation between and among factions and isolation of extremist factions with the ultimate goal of creating democratic self-sustaining states.

In a manner of speaking, that last sentence describes what we are trying to do now. But at this time we're more like the two year old with his set of blocks than we are like the master watch-maker.