do viruses make people sick or do people not washing their hands make people sic?
The virus is the root cause. The dirty hands are the proximate cause.
If there was no virus, it wouldn't matter. Ignorance is an intermediate cause.
Virii are the 'causal agent' in many cases. Removal of them will prevent people from getting sick...
Lack of handwashing spreads viruses and bacteria that can cause disease. This spread can be to oneself or others.
People not washing hands increases exposure. Over cleanliness increases susseptability.
Discussions of handwashing benefit from frequent use of the term fecal-oral to convey how disgusting not washing your hands really is.
Fun Fact: You can immediately recognize a nurse because we wash our hands BEFORE we use the restroom.
In seriousness, avoid any and all soaps and cleansers labelled "anti-bacterial". Not only do they contribute to resistant organisms, but they carry health risks to the user as well.
Fogwoman: not only are they dangerous (user health effects, increased risk of resistance) they don't really pose any benefit...
Fogwoman: I'm there only one in the family who refuses to use them and guess who's rarely sick and who's frequently sick
I never wash my hands and look at me! Totally normal.
LaLaLovely: you normal? 
You can get viruses from people who have viruses sneezing near you whether you hands are clean or not.
Fogwoman: I agree! "avoid any and all soaps and cleansers labelled "anti-bacterial". Not only do they contribute to resistant organisms, but they carry health risks to the user as well."
Actually, I thought this was a gun rights conversation between the lines. Nope... just soap.
LaLaLovely: ding ding ding!!
LaLaLovely: thank you.
Willfall: yes, she's dingy. 
Do I win a prize?
You get me LaLaLovely. 