Given that the US successfully overthrew Hussein, I don't think it is fair to say we were "defeated". It might be fair to say that we "failed". Certainly, we failed to halt a major WMD program.
But even if we concede that the overall intervention was in Iraq, I'm not sure how one could argue that Obama's command was a failure. I'm not sure if any of Obama's stated goals in Iraq weren't met-- the main one was to withdraw the troops, preferably sooner than this. If you look at Politifact's count on Obama's campaign promises, it lists only one goal for Iraq, which has been kept: PolitiFact | The Obameter: Campaign Promises that are about Military. Obama might have failed to do what you wanted to do, but he seems to have been able to largely do what he said he would (admittedly a low bar, he made many more promises about Afghanistan).
Part of the reason we are leaving now does seem to be because of the Iraqi government. When we voluntarily returned sovereignty to them in 2004 (it's been awhile, hasn't it?) we implicitly gave them the right to refuse privileges to our troops or even to order them to leave the country. That seven years later they are exercising this right, when US policy was already to withdraw troops on a similar timeline, can hardly be called a defeat.
It is a diplomatic defeat and a tactical defeat because not only couldn't we assure that our troops would be safe from unfair prosecution by Iranians with scores to settle, but leaving now means that Iran will be able to exert more influence in Iraq, the primary reason we remained in the first place.
It is a defeat plain and simple.
He picked up the pieces left by the preceding administration as best he could. I suspect that is what really annoys you the most.
No, the thing that annoys them is not only did they pick up the pieces, but Obama actually got "mission accomplished".
They're even more pissed that Libya worked out so well. It was much cheaper and didn't cost 1 American life (unlike Iraq).