The official rationale is that Syria crossed the president's "red line" by using some chemical weapons. Now that the U.S. has confirmed that use, something more significant had to be done.
The private rationale is that the rebel forces were losing and that something had to be done to prevent their collapse.
All that seems plausible to me: the president is deeply reluctant to get militarily involved, probably for many reasons. But he was backed into a corner by his own red line comments and picked the least escalatory action.
On the other hand, Dan Drezner has a very clever and plausible analysis -- that the president all along has wanted to tie down Iran and Hezbollah in a costly conflict for them, with very little cost to America. As he says:
Arming the rebels is not the same thing as a no-fly zone or any kind of ground intervention. This is simply the United States engaging in its own form of asymmetric warfare. For the low, low price of aiding and arming the rebels, the U.S. preoccupies all of its adversaries in the Middle East.Drezner is uncomfortable with this policy, but says it's better than the alternatives. Whatever the real explanation, I agree with him on that.