how do i authorize mac os montery

To add to the guidance suggested by zarathu, disconnect all other external drives and devices from the Mac. Launch the installer again and, if requested, set the drive as the startup disk, then restart the Mac and try the install again.

If that fails, see if you can get the upgrade to run in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode forces the OS to clear certain caches and logs and do other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Exit safe mode by restarting your Mac normally.

If the problem is still unresolved, please return here and post a reply and we’ll see what else we can come up with for help.

Your suggestion is not working. Still asking for "authorization". I am on a M1 Mac mini.

Frankly, very frustrating, I am using Macs since 2007, never had a problem updating the operating system. This is the first time I feel I am back at a PC, not a Mac. Macs are not supposed to have these issues and never did, until now. Very frustrating.

I am giving up on this OS update till Apple fixes this. Otherwise, I may just go back to using PCs.

Now I just have to figure out how to delete that 12 GB file from my hard drive. Any idea how to do that?

Thanks for the guidance.

However, I found something simpler elsewhere, did it without issues from an administrator account (the one I used initially was not an administrator account).

So, all taken care of. Thanks.

Go to system preferences. Click on Start up disk. Click on the lock in the lower left so you can make changes. Select it as your start up disk. Bingo.