I see the value of a strong firewall on a direct PC-Internet connection, but when the computer is sitting behind a router, I don't really see it as a necessary component of a PC's security system. This is mostly from my own experience not just with elderly users like my grandmother constantly calling me asking what she should click on the box in the corner, but more frustratingly, with firewalls mysteriously resetting themselves and forgetting their port settings, thereby completely blocking internet access on the machine until I get around to fixing it.
What exactly are the advantages of running a software firewall when the machine is already behind a router? And how shunned from the general society of well-intentioned helper-geeks should I be for recommending that people simply turn them off, provided the internet connection is passing through a router first?