I figured out what was going on. Do not do what I did and blindly copy/paste things from tutorials. Make sure you properly read up on the configuration options and know what they mean.
http://www.postfix.org/BASIC_CONFIGURATION_README.html#myorigin
This was part of my /etc/postfix/main.cf file:
myhostname = mail.mydomain.com
myorigin = /etc/
I had forgotten to complete the myorigin line or it had gotten messed up somewhere along the way. What I meant to put was this:
myhostname = mail.mydomain.com
myorigin = </etc/mailname
The < tells postfix to read that file. Now newaliases
and all of the postfix
commands work perfectly.