cPanel "Security Error" when accessing

The long answer is that Apache cannot be configured to send more than one certificate per IP because the certificate must be transmitted before any portion of the HTTP request--including the portion which specifies the hostname--is handled in order to actually secure said request. The only way to use multiple certificates on a single IP is to use port based rather than name based virtual hosts since TCP/IP will have negotiated all of that business on its own before anyone asks Apache for anything. This would require extensive manual configuration which cPanel would more than likely obliterate on a regular basis, and even if successful, anyone wishing to view the secure content would have to enter a specific, and unique, port number for each host as part of the URL. This is generally not a practical option for most people but it can be used for certain web services which are accessed by software rather than humans.

The short answer is that's the way it is and it probably won't be changing for a very long time, so accept it and move on.