Further separating the relationship between Apple and Google, the move follows the change of the inbuilt mapping facility in iOS6 from Google Maps to Apple’s own in house (bought) mapping service.
Apple’s entire statement, via The Verge, is below.
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.
Google have confirmed they will be providing a YouTube App as a standalone product shortly which will be available for download on iOS6 devices, and presumably iOS5 devices too, even though they won’t lose the inbuilt version.
A standalone App give Google some greater freedom to provide more frequent updates to the App, although it may suffer from not being as tightly integrated into the OS.