Why backup with Linux?
The question should really be “Why backup with Linux instead of Windows, if I have a dual boot PC?” Personally, I don’t dual boot, so for me the question never arises. However, I can think of a number of reasons why I would use Linux as my OS for running backups.
Windows cannot read your Linux partitions without third-party addons.
Conversely, Linux can (natively) read your FAT32 and NTFS partitions.
It is straightforward to create a backup script which mounts those partitions, backs them up, then unmounts them.
Backing up to Linux renders any virus-infected files inert.
Would you leave a Windows PC running overnight, unattended?