Why do Shiites target Sunnis if Al Qaeda is the provocateur?

"In a cycle that has been tracked by the American military since May and June, after months of apparently random sectarian violence the pattern has become one of attack and counterattack, with Sunni militants staging what commanders call 'spectacular' strikes and Shiite militias retaliating with abductions and murders of Sunnis.
. . . Maj. Gen. William B. Caldwell IV, the chief spokesman for the American command in Iraq . . . said that a recent and intensive series of American raids against Al Qaeda cells, as well as against Shiite militias that have struck back at Sunnis, had seriously damaged some of their networks." [1]

So if Al Qaeda is the provocateur in this case, why don't the Shiite militias target Al Qaeda instead of innocent Sunnis? Why don't the Sunnis and Shiites band together against Al Qaeda if this is the case?

source
The New York Times. Cycle of Revenge Fuels a Pattern of Iraqi Killings. November 20, 2006.

posted: thursday, november 23, 2006, 2:27 PM ET
update: thursday, november 23, 2006, 2:30 PM ET