Obama left Iraq? Not what I remember

I have heard several commentators say that Obama pulled out of Iraq and thereby contributed to the rise of ISIS.
That isn’t what I remember.
As I remember it, Iraq repeatedly and publicly refused to sign a Status of Forces agreement, first refusing Bush and then when Obama came into office, turned the new administration down. Without a SoF agreement, any American forces in Iraq would be subject to Iraq law while conducting operations. Something which the US rejects in all countries. As far as I know, the US has SoF agreements with every country in which the military operates.
Now, many people at the time wanted the US to stay and wanted a SoF agreement, but the Iragi civil government refused to sign. As a result the US left. Perhaps the US could have pushed harder and maybe that would have worked, but I don’t know that.

Does my memory serve correctly? I am not arguing that it was a good idea or that perhaps it could have been avoided, but do I remember correctly that the Obama administration was willing to keep significant forces in Iraq but the Iraqi government refused? Anyone have a different recollection?

That’s basically how I remember it.

However, the spirit of this argument is that Obama should have more aggressively negotiated/manipulated/coerced the Iraqi government into giving that SoF agreement. Maybe Obama could have made all future military and development aid contingent on an extended SoF agreement? The US continued to give a lot of military hardware to Iraq even after withdrawing US military forces. While we can and will argue about whether this would have been a good idea, I believe it was possible at a level of coercion short of supporting a coup to topple al-Maliki.

True. but “not trying hard enough” is a judgement call that would apply equally to both administrations. “choosing to leave” is a decision. I am wondering if others know something about the details of the negotiations that I don’t.

I’m wanting to say that his campaign platform and speeches said that we were wrong to be in Iraq, and, if elected, he would pull us out of Iraq and concentrate in Afghanistan.
Could be wrong, tho.