There is a security vulnerability in all Symantec products from Norton Antivirus to their Firewall on all supported operating systems (Windows, Linux and OS-X etc) that allows an attacker to execute code, Apparently.
So if your system was secure before, then installing a Symantec product will effectively introduce an exploitable (open to the public) backdoor.
Symantec are denying that there it is a vulnerability because nobody has exploited it yet, but that just proves what kind of professional attitude they have.