Why does Drupal say I need to upgrade to 8.0.0 beta 6 when I'm already checked out on that tag?
update.module doesn't know about git.

It only understands .info(.yml in D8) files. And .info.yml files only get their version as part of the package building process. If you look at your system.info.yml, it doesn't say anywhere that it is beta6.

There is a module called git deploy, that is trying to fill that gap and extracts version information from git and tells update.module about it, there is a Drupal 8 release but I don't know if it works with the current version.