The only way to "win" Iraq is to firebomb all of their cities, and raze them to the ground. Kill massive numbers of their citizens, and then lay waste to just about every Iraqi institution (social) still in existence, including, especially Islam.
Problem with that (besides morally of course), is that it isn't possible, and in the nuclear age, one man with one bomb can blow up a whole American city.
Imagine if say, the Chinese did that, but left one of us alive, and we found a way to get into Beijing, after the Chinese tore our natural resources away, decimated our way of life (including our religions, our individual cultures, our government). Imagine that it specifically killed your whole family, and all you had left was cold burning rage inside.
If an enemy did this to me, in the U.S., let's just say my life mission would become introducing Beijing to nuclear power up close and personal.
It's bad enough already. We've already killed alot of Iraqis, and made a bunch of enemies. For us to do what is necessary would require us to create hundreds of enemies who would want to do the same to Washington, D.C.
Do unto others as you would have them do to you is also a principle of foreign policy in addition to being the golden rule.