Time Machine is an easy-to-use backup system with features that make it the go-to backup system for most Mac users. However, like all backup applications, Time Machine is prone to bugs and issues that can cause you to worry about your backups.
Copying Time Machine backups: The volume is the wrong size for a backup error.
You can’t back up new data to a Time Machine drive that’s displaying the read-only error until the problem is fixed. There are a few possible solutions to this problem, and each takes only a short time to try.
Eject the external backup drive. If you're using an external drive connected to your Mac via USB, FireWire, or Thunderbolt as your backup drive, eject the drive from your Mac. Then reconnect the drive and restart your Mac. This is the most common solution for the Backup Volume Is Read-Only error.
If ejecting and reconnecting an external drive doesn’t help, don’t reset permissions, because that won’t do any good. Instead, follow these additional troubleshooting steps.