Because the UN voted to instigate a no fly zone so that Gaddafi would stop killing his own people and to reduce pressure on the rebellion, which was most likely going to get decimated eventually. They have a chance now, or at least create a situation similar to Kurdistan which would be protected from the machinations of Gaddafi by the no fly or no drive zone depending on how commited the UN and nato forces are.
This is also supported by Arab League. It is not the US simply going in cock sure with guns blazing. It is backed by the security council (even China and Russian didn't veto, they abstained from the vote) and the Arab League and the English and French governments were far more pro intervention then the US. This is not simply about US interests.
Now onto the usual arguement of "but but but, we didn't stop other genocides!!11" So what? Just because we didn't stop a genocide or dictators killing masses of their own people in other parts of the world means the people of Libya should be killed aswell?
What a fallacy, and so what if it co-incides with our interests? The end result of this is at least at the moment, a mad dictators military has not moved into the rebellions stronghold city and wiped them out. I think thats a good thing. And real politik is an unfortunate reality, the western powers (and probably some middle-easters countries aswell soon) don't fight where they don't stand to gain. Welcome to countries and geo-politics. Its not nice, but the result is also that Gaddafi gets a kicking and people that are fighting to remove a terrible despot get some help.
I can sleep at night under such a proposition.
