It might depend on version of OS X and/or docker, but on my machine /var is just a symlink to the real folder /private/var.
Changing the volume paths in containers/app.yml (or whatever your configuration file is) to something like:
`
volumes:
- volume:
host: /private/var/discourse/shared/web-only
guest: /shared - volume:
host: /private/var/discourse/shared/web-only/log/var-log
guest: /var/log
`
did it for me.