Unable to backup macbook using time machine

Solution 1:

Timemachine has changed a lot between different OSX versions. Some settings were still linked to an old version. The root cause appears in the Console logs. You can filter Timemachine error in Console.app by searching backupd.

In this particular case, we've figure out the error was: Illegal permissions or ownership discovered on local snapshot directory !

We've removed the local snapshot folder: solution from Macrumors

1. command-r boot to recovery
2. csrutil disable in Terminal to disable SIP
3. reboot to command-r recovery again
4. in Terminal cd /Volumes/Macintosh\ HD/Volumes (or whatever your normal boot drive is named)
5. rm -rf com.apple.TimeMachine.localsnapshots
6. csrutil enable in Terminal to enable SIP
7. reboot

And then finally, set the permissions correctly on the default "Catalina Timemachine local path":

sudo chmod -R 755 /Volumes/Macintosh\ HD/com.apple.TimeMachine.localsnapshots

And finally it works!

Main advice: Time machine error messages are not always complete. Look at logs in Console.app while triggering Backup now for full logs.

Solution 2:

As suggested, the only solution was to back up the whole system using a rsync command, and reinstall the OS from scratch.