I guess WHM is not able to create the physical certificate file. I'll just chalk it up to that being what it is.
Basically the problem is that by default cPanel ships with Self-Signed certificates for WHM/cPanel, Exim (mail), Dovecot, and FTP.
This is why when you login to whm through SSL ports, you will get a SSL warning also. Though completely secure, the certificate file itself is generated by the server and not an "approved" vendor, so there is no guarentee it can be trusted. There is a certificate in place, and the mail is secured and encrypted to the server.
The only way to remove the message your dad is seeing when he attempts to send mail is to either, A) don't use SSL or B) purchase and replace all your service SSL certificates with a valid "approved" certificate from a real SSL vendor. You would generally purchase one that matches the servers Hostname, and this would be the hostname that you would use when configuring mail.
You can also skip the whole purchasing one and get a free one from
http://cert.startcom.org/ as Jordan stated. As far as I am aware, Startcom is approved by almost all mail clients and browsers nowadays, so the popup should vanish (will also get rid of the cpanel and whm ones to get a nice free cert from startcom). Its an extra little bit of work, but it will completely resolve the issue you are experiencing.
Once you have your new fancy cert, this will show you where to install it.
Manage Service SSL Certificates