Rodger Shanahan distinguishes between the two situations:
There will of course be accusations that Obama is a hypocrite for intervening in Iraq but not Syria. That argument is simplistic and wrong. If the US is obliged to intervene militarily everywhere there is a humanitarian need, it would never stop intervening. Obama said as much in his speech. He is one of the few US leaders to understand the limits of American power. Moreover, the situation in Syria is far more complex. To have assisted one side would have meant breaching a nation’s sovereignty (no big deal) and potentially assisting the very Islamist forces that pose a security threat to the region and the West (a very big deal). The intervention in Iraq requires Obama to do neither of those things, so the calculus is completely different.
Ryu Spaeth elaborates:
As Obama made clear, this authorization of force has modest goals: 1) to protect U.S. personnel in the Kurdish city of Erbil and 2) to facilitate a humanitarian mission for 40,000 Yazidi Iraqis who are trapped without food or water and face imminent slaughter at the hands of the Islamic State in Iraq and Syria. There is no equivalent situation in Syria with such clear, executable goals.
Furthermore, the Iraqi government is a U.S. ally, as is the regional government in Kurdistan, where the latest action is happening. The U.S. has an interest in bolstering the regime and keeping it together; that is not the case in Syria. While Obama said he would prefer the Iraqi government to take the lead in this endeavor, the U.S.’s hand was forced after ISIS took advantage of gridlock in Baghdad to sow chaos in Kurdistan, which had once been an oasis of stability in Iraq.
Finally, the U.S. is partly to blame for the situation in Iraq. This is what happens when you recklessly invade other countries.
Also, Congress isn’t stopping Obama this time:
Last year, the Syrian government launched a chemical weapons attack that killed thousands of Syrians, crossing a red-line that Obama had previously laid down. In response, the Obama administration began laying out the case for launching airstrikes against positions in Syria, arguing that international norms and the word of the U.S. needed to be upheld. Congress, however, was quick to slam the brakes on that effort, arguing that their authorization was necessary before any new U.S. force could commence. The vote count soon slid heavily against Obama, with only the deal between the U.S. and Russia to remove Assad’s weaponssalvaging the situation. In contrast, Congress has yet to protest the actions, with Speaker of the House John Boehner (R-OH) saying that Obama’s proceeding with airstrikes “is appropriate.”