I was upgrading a SQL 2012 instance to SQL 2016 and the upgrade failed with the error shown below.
As you can see from the error message my account didn't have permissions on a folder. The folder in question was the default backup directory as specified on the server properties.
I knew I didn't have permissions on the backup directory, but I knew that the SQL Service account did have permissions as I had just backed up the system databases prior to the upgrade. My account was local administrator on the server and also sysadmin on the SQL Server instance.
A couple of things, it looks like the installer is checking permissions even though it is not going to take a backup, I'm not sure why it does that.
Secondly, the message "uninstall SQL Server by using this command line" is a little worrying at first, it suggests that it's going to remove the instance of SQL Server you have installed, however all it is going to do is to remove the SQL 2016 upgrade and leave you at your previous version.
So running the command line as suggested removed the failed SQL 2016 upgrade, changing the default backup directory to a local folder and then running the upgrade again and all worked fine, so the upgrade was completed successfully.