Something must have changed recently with how cPanel handles addon domains. I've added 2 other addon domains "under" the server's domain (yet not it's hostname, which is a subdomain of the server's domain), and didn't have a problem. This time I get the same error, You do not have permission to create subdomains of the server's hostname.
It seems enabling ""Allow users to park subdomains of the server’s hostname" is the resolution (as stated by cPanelMichael and from my own experience just now), but that terminology is wrong.
apollo.maindomainname.com is the hostname
maindomainname.com is NOT the hostname
maindomainname.com is where I was trying to create a subdomain, in order to create/add an addon domain. I've done it before, I know it is possible
So that's part of what's confusing people, it that cPanel is using the wrong terminology in the Tweak Settings.
There's also the addon vs parked issue, because to those of us who also sell domain names, "parked" means something different than it does in cPanel. It would be really, really, really, REALLY nice for cPanel to offer a means of parking (I mean really parking, not domain forwarding that cPanel calls parking) domain names. I realize cPanel is for hosting and assumes that anyone who buys a domain name also buys hosting, but it doesn't always work that way.