Same issue here. Mine is a MacBook Pro (not retina) 2012. I upgraded the hard drive like a year ago (before el capitan) to an SDD 500GB drive and encrypted the file system.
Everything was running smooth, so i decided to upgrade to sierra last night. The installer downloaded ok from the appstore, i started the installation, but after it rebooted, the installer app stalls and shows a message stating that "macOS could not be installed on your computer" - File system verify or repair failed. - Quit the installer to restart your computer and try again.
Here's the error:

Obviously i opened the "Disk Utility" app to check the file system on my disk, getting also an error, stating that the file system could not be repaired after 3 attempts. This is really weird because as i said, the system was running just fine, before i tried to upgrade.
The real problem here is that the computer entered in a loop that i can not get out. When i click in the restar button, the computer restarts but always tries to resume the installation, stalling at the same point, over and over again.
So, the question is: can i avoid the installer to restart every time i reboot the computer? or there's already a permanent damage to the elcapitan osx and it will not boot again?. In the worst case scenario, i'll be forced to try to move my data to an external drive using the terminal interface available through the installer app, because the files are encrypted and i can not recover them directly without entering the password for decryption.
Thanks in advance for any tip.