Apple TV doesn't play some youtube movies
The reason your favourites do not appear in the listing on the Apple TV is that the owner of the video has not allowed it to be viewed on a mobile device (which the youtube considers the apple TV to be). The Apple TV recognises this and removes it from the list so you do not try and play an unplayable video.

The owner of the video (or more probably the copyright owner of the soundtrack) can decide whether to allow mobile devices and Apple TV's to display videos.