Library without iCloud

If you don’t want to activate iCloud Music Library, then you will need to get content from the iTunes Store or sync music from iTunes on a computer (not involving an Apple Music subscription).

With an Apple Music subscription, you cannot add music from the Apple Music catalog to your device library without iCloud Music Library. An Apple Music subscription without iCloud Music Library doesn’t utilize the library at all (only For You recommendations, Browse, Radio, and Search).

Turn on iCloud Music Library with Apple Music - Apple Support

Access your music collection on all of your devices with Apple Music - Apple Support

The iCloud Music Library only lists the music tracks. The hosting of the music files is not counted against your personal iCloud disk space. If you want to download all collected Apple Music tracks to your device, then you need to go through the iCloud Music Library; no way around that.

If you have specific objections against iCloud use, then please elaborate.

it assumes I want the same library across my devices

Yes it does. But don’t think of the iCloud Music Library as you know it from the ‘traditional’ music library and syncing with that. See the iCloud Music Library as a listing of tracks, not the files themselves. The files can be in the cloud (Apple servers, but not your personal iCloud space), or on your device, in any mix you want. If you want 5 albums by artist X on device 1, and 6 albums by artist Y on device 2, then that is your choice. But all of your collection is listed on all of your devices, and any changes (removal or additions) are synced automatically.

it requires cloud access

Yes it does. But you can still download tracks for offline use per device, as a sub-selection from your iCloud Music Library (“master library”).

I'm using iTunes to share parts of my offline music library with my iPhone and my iPad and I have different collection of offline music on my devices.

The Apple Music service gives you that option, as I hope to have shown above.

I simply can't find any valid reason for not being able to story my collection (list of albums) on my own device and I find it mind boggling.

Again, if you don't wish to pay Apple to provide this service, you'll have to find or build one yourself.

You'll need a storage place online that will stream Music tracks to an app on your device that will accept the stream.

This Requires iCloud Music Library".

Meaning that you are asking for a service you don't want to pay for.

Best of luck.

It is not a restriction. It’s how Apple Music works.

you can stream only if you don’t want an iCloud music library to reference.

if you wish to stream iTunes purchased or your CD based music, you need a library.

does that clear it up for you?

I should be able to build my own music library on my own devices without forced to use another service, and it should be my decision whether I want to sync it with other devices or not.

You are absolutely allowed to do this any way you wish. You are not forced to do anything.

I don't believe any 3rd party offers a streaming service for you using your own music.

Apple offers 2 ways. The most cost effective is easily iTunes Match at $25 /year and allows up to 100,000 tracks in your iCloud Music Library.

You seem to know about using iTunes to stream your music for free within your now home network.