How to deauthorized old computers ?

See the following from Authorize or deauthorize your computer for iTunes Store purchases - Apple Support

If you need to deauthorize a computer that you don't have access to

To deauthorize a computer that you don't have access to, you have to deauthorize all of your computers. Then authorize each computer that you have again. You can deauthorize all computers only once a year.

1. Open the Apple Music app or Apple TV app.
2. Choose Account > Account Settings.
3. Sign in with your Apple ID and password. Forgot your Apple ID?
4. At the top of your Account Information page, go to the Apple ID Summary section.
5. Next to Computer Authorizations, click Deauthorize All.
6. Authorize each computer that you use again.

PS: as a result of this I can't listen to music for which I still possess the original CDs. This is so ridiculous and to be honest it enrages me against the companies that do this, starting with Apple. Stop acting like a nanny gatekeeper and start acting like a mother flipping service provider.

That's as may be, and it's a logical theory.

Yet I can't play the music that I loaded via CD some time ago (before this Macbook was even born).

This is what I get when I try to play my own music.

TRexAccordion wrote:

PS: as a result of this I can't listen to music for which I still possess the original CDs.

Authorization has nothing to do with being able to play your "original CDs" (physical CDs), importing them into iTunes/Music, playing them in the iTunes/Music apps or even burning their playlists to additional CD media.

Authorization only pertains to being able to play music or video that you have purchased directly from Apple and that have DRM associated with them. Not all purchases from Apple even have DRM.