Could my firewall or antivirus software be causing FF14 error 16a?

Yes, your firewall or antivirus can sometimes block FF14's communication with the servers. Temporarily disable your firewall and antivirus (one at a time) to see if the error resolves. If it does, you'll need to add exceptions for the FF14 launcher and game executable to your firewall/antivirus settings. Consult your software's documentation for instructions.