Earlier quoted context omitted.
It's against the YouTube terms of service. One characterization of this software is that it is designed to violate the YouTube terms of service. "The following restrictions apply to your use of the Service. You are not allowed to: access, reproduce, download, distribute, transmit, broadcast, display, sell, license, alter, modify or otherwise use any part of the Service or any Content except: (a) as expressly authoriz…
This doesn't really explain anything. Why is Apple enforcing YouTube's terms of service on a third-party application? Especially via a mechanism ostensibly designed to stop malware. Is the Transmission torrent client next because it could be used to download copyrighted content?
5.2.3 Audio/Video Downloading: Apps should not facilitate illegal file sharing or include the ability to save, convert, or download media from third-party sources (e.g. Apple Music, YouTube, SoundCloud, Vimeo, etc.) without explicit authorization from those sources. Streaming of audio/video content may also violate Terms of Use, so be sure to check before your app accesses those services. Documentation must be provided upon request.
https://developer.apple.com/app-store/review/guidelines/#int...
As to the why, because Apple could be sued by third parties for allowing this behavior for apps that Apple has vetted.