Why do I have to pay to listen to my music library on itunes?

You don't. There is an optional subscription service that lets you match or upload your content to the cloud so that you can use it on your device without directly syncing with iTunes, potentially giving you access to a larger library than would fit on it. Apple Music also gives you the ability to download or stream almost anything from the iTunes Store. See Sync your iPhone, iPad, or iPod using iTunes on your computer - Apple Support to sync with your library.

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