Follow the steps below to fix the problem of Apple Music not showing up in iTunes on Mac
Open iTunes on your Mac by clicking on the iTunes icon in the Dock of your Mac.
iTunes Icon in the Dock of Mac
Next, click on iTunes tab in the top Menu Bar of your Mac and then click on Preferences… option in the drop-down menu (See image below)
iTunes Preferences ...
The music available on the iPhone is not shown in the iTunes when you click on the iPhone icon in the iTunes toolbar.
The music should be present in your iTunes library (if you originally synced it from iTunes to your iPhone). This is by design and how syncing music from iTunes to iPhone works.
You need to connect your iPhone to the computer with iTunes ...