I'm neither an expert on the View nor O'Reilly, but I thought it's been a running thing (like with Letterman/O'Reilly and Stewart/O'Reilly). I agree though. Barbara knows her stuff, and it's her show.
To summarize the posts above, "The side I agree with punked the other." Barbara Walters punked them all.
O'Reilly and Baba Wawa worked together for over a decade at ABC, and are very likely longtime friends. I think the whole thing was contrived. It helps O'Reilly sell books, and generates some publicity for the View.
It's show business. He goes on those idiot and meaningless shows, throws some insults, two ugly hosts walk off (99% chance it was pre arranged) and now he's back in the limelight and ratings for his show go up. It's acting.
Okay, here's the shot out of the cannon: Oprah, Barbara Walters, your wife. You gotta fuck one, marry one, kill one, go!