The reason the Islamic State (aka ISIS or ISIL) is so hard to defeat is that so many Middle East leaders are more fearful of Iran than of ISIS.
The Middle East is divided by a conflict of alliances superimposed on a conflict of religious factions, and both sides are more concerned about their relative power than about ISIS.
One side consists of Iran, a theocratic Shiite state, which supports the Shiite-backed government of Iraq, the Alawite-backed government of Syria, Shiite militias in Iraq and Hezbollah, the Shiite militia in Lebanon.
Arrayed against Iran are Saudi Arabia, the Gulf emirates, the Sunni militias in Iraq and Syria and, implicitly, Israel. There also are the Christian Arabs, the Kurdish people and others who are caught in the middle.
ISIS grew out of Sunni militias, who were fighting in Syria against the government and in Iraq against the Shiites. What makes ISIS a problem for the anti-Iran coalition is that they not only persecute Christians and Shiite Muslims, which has been going on for a long time, but also other Sunni Muslims who don’t accept their version of the faith.
The Saudis, Gulf emirates and Turks would like to get rid of ISIS, but not to change the balance of power in favor of Iran and Syria.
The U.S. government has the same problem. Washington wants to destroy ISIS, but for a long time was unwilling to give up the hope that there are “moderate” Sunni militias that would overthrow the government of Syria. So Washington kept sending arms to Sunni rebels in Syria which wound up in the hands of ISIS.
The Iranian government has for years been the enemy of America’s chosen enemies—the Taliban in Afghanistan, the Saddam Hussein regime in Iraq and now ISIS. Washington has ceased waging economic warfare against Iran, but has not ceased trying to checkmate Iranian power in the Middle East. But so long as Iran is held in check, ISIS is likely to survive.