Obama's number one goal right now is re-election. To paraphrase something someone once said, the first victim of a re-election campaign is the truth. Here are a couple of things to keep in mind each time you hear "Obama is pulling our troops out of Iraq":
1) The agreement under which the troops are withdrawing was signed in 2008. Does anybody remember who was president in 2008? I'll give you a hint. It wasn't Obama.
2) The Obama administration has been trying to extend the agreement and postpone withdrawal. Specifically, Obama wanted to keep 5,000 military "trainers" in Iraq. The Iraqi Parliament refused to approve that plan or to approve the US demand that the troops be given immunity from Iraqi law. So, this is sort of a case of Obama saying to the Iraqis, "You can't fire me, I quit." Nevertheless, Obama is still trying to negotiate an agreement to allow the trainers to stay.
3) As the troops leave, the State Department is beefing up a security force that will be manned by thousands of contractors who will be armed with aircraft, armored vehicles, and other military hardware. See this article for more info about that:
http://www.mcclatchydc.com/2010/07/21/97915/state-dept-planning-to-field-a.html
So, Obama is being forced by the Iraqis to implement Bush's plan. That's the bottom line regardless of how each side tries to spin it.