The problem is, traditional viruses don't really exist any more. Nowadays, lame crackers are busy making trojans and worms, so that's what anti-virus programs try to tackle now. The problem is, with everybody online these days, trojans and worms are fast to spread and easy to modify, so anti-virus programs are useless in trying to prevent them. If you're lucky, then can remove the infection after the fact, assuming your disk isn't so messed up there is nothing left to disinfect. Oh that's not all.
Firewalls are network barriers designed to keep out crackers.
Since file downloads are a normal part of your internet experience, however, personal firewalls can't stop you from downloading the trojan that installs that backdoor in the first place.