/home/user: change directory failed error

You need to tell useradd to create your home directory:

useradd -m fox

You might also want to add options for group(s) -g -G, login-shell -s etc.

But don't worry - you can create your homedir now (as root using sudo or su):

# mkdir /home/fox
# chown fox:fox /home/fox

See Arch Linux Documentation - User Management

It's actually a SELinux issue. Not sure about Arch Linux's configuration but I encountered it when replacing my home directory with another (i.e. restoring it from a backup). You can check it yourselves with

ls -lZ /home

That prints out SELinux labels. Your home directory should have the user_home_dir_t label. The fix is straightforward:

restorecon -R /home

A longer discussion can be found in the Fedora forums.