Security is not a product you can buy and install and hope it takes care of everything.
Security is not an operating system that you may think is more secure than some other.
Security is an ongoing process of eternal vigilance. Of keeping your wits about you and being aware of impeding threats.
Trusting your security to some AV company is as dumb as those hotels that trusted electronic locks on their room doors. (Google it)
Good news is that AV software can detect old threats.
Bad news is that it is the new threats that will get you.
You are probably misunderstaning my point:
I am the one who distrusts advices like having just to change the password, and I am the one who fears that the suspected virus security of Linux is overestimated today (and even more so in the future), and therefore I am the one who thinks that further security is necessary now and in future, just as it is already common on Windows systems: that means the need for antivir and anti-malware software, just like already available for Windows. Probably there is currently not such an approved and failsafe security software availble yet for Linux of exactly those reasons, but I think we'll see what will happen in the coming years if the number of common (non-IT, non-CS) Linux consumers will be quickly increasing.
PS, as to "Bad news is that it is the new threats that will get you":
if new virus software or malware has been detected, the AV databases become quickly updated - unprotected users will be widely infected furthermore, whilst AV users are protected then.