I love Jon Stewart, but he's guilty of being both six months late to realizing the contradictions of our foreign policy, and for dramatically oversimplifying it.

Yes, I said oversimplify. You see our middle east policy is far more convoluted than that 2-minute video could possibly encompass.
Allow me to explain.

Richard Engel tried to sum up our current Iran policy this way.

In Iraq we are fighting with Iran [against ISIS]. In Syria we are both with and against Iran, and in Yemen, now we are backing Saudi Arabia and Egypt and this other coalition against Iran, but we say we aren't going to get deeply involved.

Now you might be under the incorrect assumption that we joined with the Saudi-led coalition against the Shia Houthis in Yemen for some strategy or moral reason, but you would be mistaken. You see, until recently we were trying to becomes the Houthi's BFF, or at the very least we didn't want to fight them.
The problem was that the Houthis just weren't into us.

“Although the Houthis have seized control of much of the country and are avowed enemies of al-Qaeda, they can’t project power against the militants the way the Hadi government could with American support, officials say. Deeply anti-American, the Houthis have rejected U.S. overtures, officials say.”

Only once we were rejected did we join in the anti-Houthi alliance.
The thing is that the Houthis have already effectively destroyed its opposition, with the exception of al-Qaeda in Yemen, so the Saudi airstrikes are unlikely to shift the balance of power and will damage our long-range objectives. What's more, both the Houthis and al-Qaeda have seized hundreds of millions of dollars worth of American weapons.
That leaves us fighting both al-Qaeda in Yemen and their biggest enemies in Yemen, the Houthis with little chance of either side winning based on the current strategy. Or as Jon Stewart put it, "a proxy war against ourselves."

Jon Stewart got confused about the Iraq v. Yemen part, and for good reason, but that isn't even close to the most confusing and contradictory part.
It's Syria where the story gets absolutely baffling.

Let's start with Joe Biden's "gaff".

Biden made the most basic mistake you could make in realpolitik: he told the truth.
You can't come out and say that your Gulf allies are arming and funding baby-killers. At least not in "polite society".
What Biden didn't say is the obvious conclusion; that our Syrian policy makes no sense.

In Syria, the U.S. and Iran are on a clearer collision course. While each again speaks of combating the Islamic State group, they clash on their views of the Syrian government and the country’s four-year rebellion.
The U.S. is arming and training a primarily Sunni force described as moderate, working with Sunni states such as Saudi Arabia, Turkey and Jordan. The rebels have the double objective of defeating the terrorists and ousting President Bashar Assad from power.
On the other side, the Iranians are providing military assistance to Assad’s army and Hezbollah forces fighting the rebellion, and have deployed special forces of their own to help out.

Of course American-supplied weapons have wound up in the hands of ISIS again and again and again, so it's not like we have the moral high ground.
In fact, the Iraqi Army has even allegedly shot down an American helicoptor for supplying weapons to ISIS.

It would be a big mistake to ignore any incidents of the anti-ISIS forces in Iraq threatening American forces. After all, there is a history of bad blood between Shia militias and Americans.
Which brings us to the next contradiction of our current war policy - our allies hate our guts.

“We will respond with force while they are within our firing range,” Shibil al-Zaidi, a leader of the Kitaeb Imam Ali militia, said in a statement about the alleged U.S. strike on Friday. “We have the ability to face these American attacks.”

The thing is that this is the second Iranian-sponsored Shia militia to threaten to kill Americans in the last few days.

“We are staying in Tikrit, we are not leaving and we are going to target the American-led coalition in Tikrit and their creation, ISIS,” said Akram al-Kabi, the leader of the Nujabaa Brigade, a powerful militia that has previously sent fighters to Syria on behalf of the Bashir al-Assad government there.
His remarks raised the possibility that the group would use antiaircraft fire against coalition warplanes, using Iraqi fighting positions.

Al-Kabi was once a deputy in Asaib Ahl al-Haq and was associated with that militia’s attacks against U.S. and British troops in 2008-2011.
What kind of war can we possibly fight when our "allies" will try to kill us when they get a chance? And what sort of allies are they?

All of which raises the question: Does the United States have a “common interest,” as Secretary of State John Kerry phrased it, with a regime in Tehran whose proxies are currently burning people alive in their houses, playing soccer with severed human heads, and ethnically cleansing and razing whole villages to the ground?

Whatever they are guilty of, that hasn't stopped the United States from giving them Abrams tanks, Humvees, armored personnel carriers, MRAPs, and rifles, all on the bill of the American taxpayer.

For any of you who still believe that fighting alongside our headchopping, ethnic-cleansing, user of power drills on skulls, Iranian-led Shia militia allies makes a bit of sense, consider what this Iraqi army general has to say.

“Many of the people in Mosul will stand with [the Islamic State] if Shiite militias invade,” said Gen. Najim Jibouri. “Eighty percent of the population is does not like [IS], but if the militias are involved — 80 percent will stand very strong with [IS]. I told the Americans before, the image now is not like it was in 2003. Now the Sunni people want American forces. They will throw the flowers on them now, because the battle now is not between them and the United States and [IS], it’s between the Sunnis and Iran.”

However, the true insanity is in Syria.
Let's not forget that our "big plan" for Syria is to train 5,000 "vetted, moderate" rebels to bring down both ISIS and Assad, a plan that Chris Harmer calls "laughable" based on its size.
That isn't the only problem with this plan. There is also our long-standing inability to back the correct groups in wars.
Even in Syria we've had issues. Consider al-Qaeda in Syria, also known as Nusra Front. They are still backed by Qatar, eventhough we are currently bombing them. al-Nusra destroyed not one but two of our "moderate rebel allies" and seized all their American-made weapons.
al-Qaeda used those weapons to seize an entire province of Syria and become the most powerful military force in north-western Syria.

The situation in the middle east is unprecedented. For the first time since WWII, almost every country from Libya to Pakistan is currently at war. Unless chaos was the objective, our current strategy isn't working, or can even by defined.