You're right about the "black/white" part, but the part about combating insurgents is not really accurate. The "terrorists" didn't exist in Iraq until after Saddam was deposed. Saddam never killed Islamic radicals, he never had to worry about them. The American invasion radicalized the Muslim world and radicals rushed into Iraq to fight against the Americans. The same thing happened in Afghanistan when the USSR invaded in 79.
And after the idiot Paul Bremer disbanded the Iraqi military, all of those former Saddam military leaders and secret police became unemployed and desperate. All they know is murder and intimidation, so naturally that's going to be the skill they use to survive now. These were all people who didn't give a shit about islam or jihad -- but they lost their paycheck (lost their future) and they were terrified of revenge from the Shiite majority (Shiites are 60% of the population and had been Saddam's favorite victims -- Saddam killed them in order to control the oil-rich areas where they lived and cheat them out of the wealth their land produced).
So these former non-religious Baathists used the Al Qaeda religious message (fight against the Crusaders and the Apostates -- the Americans and the Shiites) to bring in donations and soldiers. They used the religious identity to recruit an army so that they could carve out a future for themselves against the more numerous Kurds and Shiites. And they started calling themselves Al Qaeda in Iraq. I think their ultimate goal was to just control enough of the Iraqi oil to force the world to deal with them, the way the world dealt with the Saudis.
The only reason this temporarily calmed down was because the Americans started buying off the Sunnis in Iraq and convincing them that the Shiite government would give them a fair cut of the oil money. That made things quiet down for awhile -- though it never really stopped. Zarqawi died and al-Masri died, but AQI continued. In the meantime, shit got worse again -- the recession happened, and there was a major drought in the middle east, and the Shiite government never really came through on any of their promises for bringing Sunnis into the government or sharing oil profits. The Syrian civil war started and AQI went to war against the Iranian proxy Bashar al Assad. They later became ISIL. And here we are.
Basically we can call them "radicals" or "terrorists" now because they use an Islamic fairy tale to bring people to their cause and inspire people to commit terrible violence. But it's all just desperate people fighting to hold onto power and control resources -- the same as it was under Saddam. The difference from the Saddam era was just that Saddam had a monopoly on power so he could crush the Kurds and Shiites. Now the Kurds and the Shiites are capable of holding their own. The Sunnis and former Saddam loyalists are using the only weapon they have -- radicalization.