I think Bush Jr did the world a huge favor by invading Iraq. That was the trigger which set the dominos in motion, and out of the chaos freedom and democracy is rising.
Agreed, but there are two major questions here. (1) Is Islamic democracy doing the world a favor? I support their right to democracy, but it's not yet clear that democracy will benefit the world along with themselves. And (2) was this invasion necessary to achieve the same result? There's an argument to be made that everything demonstrated and accomplished by invading and reforming Iraq could have resulted from Afghanistan, also a Muslim nation reformed to democracy. (We don't know for how long, but then we don't know that about Iraq either; fledgling nations are always a crap shoot.)
I agree with this regarding Obama not being able to keep Mubarek in power, and that condemning him and asking him to step down was the obvious move. However, I don't recall there being specific support for the Brotherhood in particular. The US government supported Mubarek leaving and then free and fair elections. After Morsi was elected, we then recognized him as the legitimate head of state. Not quite the same thing as backing the Brotherhood in the elections themselves. But then my recollection could be in error here.
Honestly "support" might be the wrong term. "Work with" might be closer, as only the Muslim Brotherhood had any existing organization and were by default the de facto government. The point is the same though. Obama walked a tightrope of supporting Mubarak while also supporting democracy. Once it was clear that Mubarak was going, Obama switched to asking Mubarak to step down. After that Obama worked with the Muslim Brotherhood during the transition, and afterwards supported Morsi as legitimate ruler.
The US has three sometimes-clashing interests here: Promoting democracy, promoting the best relationship possible with whatever government emerged, and maintaining Egypt in particular as an ally even if necessary around the new government, to the extent that a Middle Eastern Islamic nation can be a US ally. Preserving Mubarak was in service to the latter two interest but in conflict with the first. I think you and I agree that within the existing events and considering those parameters, any President would have done much the same, regardless of how much we may dislike the results. His actions are constrained by our national interests, whereas mine as an unempowered peon are not.