It's true that basically no one believes that this will turn the tide of the Syrian war. But this is important: it's not supposed to. The strikes wouldn't be meant to shape the course of the war or to topple Assad, which Obama thinks would just make things worse anyway. They would be meant to punish Assad for (allegedly) using chemical weapons and to deter him, or any future military leader in any future war, from using them again.
8. Come on, what's the big deal with chemical weapons? Assad kills 100,000 people with bullets and bombs but we're freaked out over 1,000 who maybe died from poisonous gas? That seems silly.
You're definitely not the only one who thinks the distinction is arbitrary and artificial. But there's a good case to be made that this is a rare opportunity, at least in theory, for the U.S. to make the war a little bit less terrible - and to make future wars less terrible.
The whole idea that there are rules to war is a pretty new one: the practice of war is thousands of years old, but the idea that we can regulate war to make it less terrible has been around for less than a century. The institutions that do this are weak and inconsistent; the rules are frail and not very well observed. But one of the world's few quasi-successes is the "norm" (a fancy way of saying a rule we all agree to follow) against chemical weapons. This norm is frail enough that Syria could drastically weaken it if we ignore Assad's use of them, but it's also strong enough that it's worth protecting. So it's sort of a low-hanging fruit: firing a few cruise missiles doesn't cost us much and can maybe help preserve this really hard-won and valuable norm against chemical weapons.