Why does a sweaty finger neutralise the touch-sensor on my phone screen?

Most phone screens are capacitive. They work by sensing the change in capacitance due to a nearby conductive object.

I can't imagine a way in which simply having some sweat on a fingertip would interfere with this mechanism. I can't reproduce the problem with my phone and a glass of salty water.

However, I'll offer a guess as to what's happening: if you get enough sweat on the screen, the phone will have difficulty distinguishing what is a finger, and what is a gob of sweat. To the phone, broad contact over large areas of the phone look a lot like the side of your face, so the phone ignores these touches since mashing keys with your face is usually not desirable.

I've experienced your problem too. My hands sweat a little bit more than average, and while my phone screen is 'wet' its ability to tell my actions touch/swipe diminish. So, I just tested this on my Samsung S3 (which has a capacitive touch screen).

All it took for this problem to arise was sparkling some water on its screen and trying to do any actions like going back, pressing apps, etc. It got either confused or refused to act upon my actions.

So, first we have to know how capacitive touchscreens work. To quote "Good Gear Guide":

Capacitive touchscreens work by sensing the conductive properties of an object, usually the skin on your fingertip. A capacitive screen on a mobile phone or smartphone usually has a glass face and doesn't rely on pressure.

That means that if you get a conductive substance, like water or sweat, in the way, it fails to detect your actions properly.

Borrowing an explanation from Embedded for capacitive devices that are neither water tolerant or waterproof, like my cellphone (and I guess yours too):

Fingers [and Water] are conductive, so they interact with the electric field that is set up around the touch sensors. [Water drops can produce] the same signal level as a finger for a touch sensor that lacks any features for water tolerance, even when no finger is present. (See the image below.)