Why did Barack Obama say "my Muslim faith"?

I've seen so many mentions of this in the comments to various posts here today that I can see I need to break this story out into a separate post. Here's the video, from "This Week" with George Stephanopoulos:



The Washington Times has the transcript and a description of how a snippet of the interview has caught fire on the internet:

Within an hour of the interview's broadcast, anti-Obama groups were pushing the issue on blogs and via YouTube.

Someone spliced together only his misstatement and was emailing it with the false claim Obama "admits" the Muslim faith.

It's clear in the full context that he's giving the McCain campaign credit for not participating in spreading the rumor that he is a Muslim. He's not saying he is a Muslim. Quite apart from that, let's not stoop to portraying "Muslim" as the equivalent of evil. That's ugly and destructive.

UPDATE: More here.