Get Religion makes a good point about “traditional Iraqi values.” This story also makes the point which needs to be stated over and over again, “honor killings” and the like are not a fringe part of Islamic custom and mores, they are the very essence of what Islam is all about. There is no way you can Westernize Muslims and have them remain Muslims. The Koran is wedded to the Century (7th) in which it was written. Beheading people is not endemic to Muslims, it’s part and parcel of those times, be they Muslim, Christian, or anything else. The problem, though, is being a faithful Muslim means being faithful to the culture of the 7th Century. To ignore that is to ignore reality. Do you really think the father of the girl in this story is an Islamic extremist, or living in the USA (and an American citizen) he is more likely representative of mainstream Islamic belief?
UPDATE: A commenter at Get Religion gets it right:
It is important for reporters to note how “honor killing” is supported in Islam — under Islamic/Sharia Law, parents who kill their own children are not prosecuted for murder.