The "why" of it's actually pretty easy: a stable Iraq in the US sphere of influence puts pressure on Iran and Syria and has the potential to stabilize the entire region, just through the fact of geographic location.
But more importantly, an unstable Iraq at war with itself destabilizes the entire region, much the same way the Afghan civil war in the '90s caused problems for the Central Asian Republics (and Pakistan and even Iran). But I imagine an Iraqi civil war would be worse; rather than focused around shifting tribal alliances as in Afghanistan, it would be along clearly delineated ethnic borders, and I can't see how neighboring countries could avoid getting involved. When the Kurds and Iraqi Shi'ia start fighting, for example, how could Iran not avoid supporting the Shi'ites, and will Turkey deny its own Kurdish regions the ability to support the Iraqi Kurds (thus importing an Iraqi Civil War to its own soil, in effect), or turn a blind eye (risking direct conflict with Iran)? Syria will support the Ba'athist remnants, the Saudis the Sunni fundamentalists, everyone with a grudge agains Jordan will use western destabilized Iraq to attack them...
Frankly, I kind of feel about the occupation the same way I feel about Musharraf ruling Pakistan. Yeah, it's hardly an ideal situation...but you really don't want to see the alternative.