You didn't answer my question. That just tells me that we can maybe preserve the norm against chemical weapons, not why we should.
Fair point. Here's the deal: war is going to happen. It just is. But the reason that the world got together in 1925 for the Geneva Convention to ban chemical weapons is because this stuff is really, really good at killing civilians but not actually very good at the conventional aims of warfare, which is to defeat the other side. You might say that they're maybe 30 percent a battlefield weapon and 70 percent a tool of terror. In a world without that norm against chemical weapons, a military might fire out some sarin gas because it wants that battlefield advantage, even if it ends up causing unintended and massive suffering among civilians, maybe including its own. And if a military believes its adversary is probably going to use chemical weapons, it has a strong incentive to use them itself. After all, they're fighting to the death.
So both sides of any conflict, not to mention civilians everywhere, are better off if neither of them uses chemical weapons. But that requires believing that your opponent will never use them, no matter what. And the only way to do that, short of removing them from the planet entirely, is for everyone to just agree in advance to never use them and to really mean it. That becomes much harder if the norm is weakened because someone like Assad got away with it. It becomes a bit easier if everyone believes using chemical weapons will cost you a few inbound U.S. cruise missiles.
That's why the Obama administration apparently wants to fire cruise missiles at Syria, even though it won't end the suffering, end the war or even really hurt Assad that much.