In iOS 6 beta 4, Apple decided to remove the standard YouTube.app which was part of the stack of apps that the phone came with, ever since they’ve released it back in 2007.
Apple’s statement on this matter is:
Our license to include the YouTube app in iOS has ended, customers can use YouTube in the Safari browser and Google is working on a new YouTube app to be on the App Store.
Engadget has heard from Apple and learned that while iOS 6 devices will lose the stock YouTube app, iOS 5 devices will not.
It seems that either Google’s licensing agreement permits it to stay on the older OS, Apple didn’t want to go to the trouble to push out a point update that takes away a feature, or some combination of both.