Why is Barack Obama bombing Syria?

He really doesn't, based on statements he has made. He has said that military force would be a last resort, if Syria's president refuses to stop using chemical weapons against his own people. The majority of the world community long ago agreed that the use of chemical weapons is forbidden, so President Obama said that since it was indisputable that Mr. Assad had used these chemical weapons, there had to be consequences. However, Mr. Obama repeatedly stated that he prefers a diplomatic solution, and if there is such a solution, there will be no military response. If no diplomatic solution can be reached, then he would be willing to consider a limited military action, directed against the places where these weapons are produced or stored.