Is it any of our business that Syria use chemical weapons? I’d say yes. Here is why.
A) Chemical weapons are prohibited by international law. The use of poison gas is a war crime, prohibited by the Chemical Weapons Convention (CWC). The United States is a logical enforcer of this law. We are a signatory to the treaties, and a permanent member of the UN Security council. We are also one of the few superpowers in the world and we have been considered the military leader of the free world since WWII.
B) Chemical weapons are a war crime and their use is intrinsically evil. While the United States cannot reasonably police every act of evil in the world, we do have the capacity of monitoring and punishing a limited amount of particularly evil acts. e.g. the resumption of slavery, the use of weapons of mass destruction, etc. As a well established war crime, the use of chemical weapons against civilians (including a hospital that was deliberately targeted) falls into this category.
C) The use of chemical weapons poses a unique risk of collateral damage to the international community. Collateral damage to nonparticipants in a war always risks military reprisals (see our declaration of war against Germany in WWI over their use of unrestricted submarine warfare.) The use of weapons of mass destruction risks extreme collateral damage to civilians. Some studies have shown that large scale us of chemical weapons could cause more civilian deaths than a nuclear exchange. In view of the risks posed to the world by the use of chemical weapons, the United States has a clear interest in strongly discouraging the use of chemical weapons.
From whom much is given, much is required. The military action taken by the USA was a logical and reasonable response to a the use of Chemical weapons by Syria. Following in the tradition of the old English empire using their military to abolish the slave trade, it it is incumbent upon the United States to use our status as a world power to punish obvious acts of evil like this.