Why should you remove metallic jewelry before working on batteries?

Because you really don't want to short out the circuit through your jewelry.

I was once working with a six volt lantern battery and my screwdriver slipped, briefly coming into contact with both poles of the battery. There was a brilliant white flare and, in the fraction of a second that the screwdriver was touching both poles, the arc melted halfway through the shaft. In fairness, this was a small screwdriver, but still I'm extremely glad this didn't happen to something I was actually wearing at the time.