Below is a photo of the electro-mechanical soap dispenser in the bathroom of my office building. Notice how it has dismantled itself, so soap is no longer dispensed. An entire floor of workers has stopped washing their hands, and it’s just a matter of time before someone gets sick.
As Jude Law learned the hard way (see photo below) in Contagion, it just takes one sick person to start a massive epidemic, killing off vast quantities of humans. If (when?) Skynet becomes self-aware, how do we know that the smoking gun will be in the shape of a mushroom cloud? Maybe it will be in the shape of a sneeze or a cough, a high fever and some agonal spasms.