I still cannot figure out why. Gaddafi was not causing trouble.
A lobbyist “wanted it”. Obama had to be talked into it by Hillary.
Not only was he not causing trouble anymore, Gaddafi might have been "turned" to a US asset.
Remember how Gaddafi turned over his entire nuclear program to the US? This was just after Bush invaded Iraq. It turned out Gaddafi had been secretly developing nuclear weapons --apparently unbeknownst to our intelligence agencies-- and the project was well underway. After the invasion of Iraq, Gaddafi surrendered it all to the US. The dismantled pieces of Libyan nuclear hardware were transferred to a storage site in Tennessee. But the media conveniently ignored or denied this side-benefit of the invasion of Iraq.
And unsavory as he was, his presence kept Libya from falling into the hands of the radical Islamists.
"We came, we saw, he DIED" quoth Hillary. Yes, it was her vainglorious attempt to establish a tough image, and to cement a legacy as Secretary of State, that resulted in the HOT MESS that is Libya today -- a mess that includes a stream of Libyan refugees crossing the Mediterranean to Europe in rickety boats.