In order to skim a stone, it must be spinning and tilted slightly so that its leading edge is a bit higher than its trailing edge. This means the trailing edge will hit the water first. But because the stone wants to keep spinning along the same axis, the whole stone will skip up instead of just the bit that hit the water. And it will keep jumping as long as the stone is spinning. In effect, the spinning stone is like a gyroscope.
Gyroscopes try to keep spinning in the same direction.
So rather than tilting over when the stone hits the water, it jumps up to keep its axis pointing in the same direction. You can't skim a round stone because there's no trailing edge to hit the water, and you can skim a stone that isn't spinning because it just sinks. There's no gyroscope effect to make the stone skip. This is a stand-alone question which will eventually become integrated into the linked database.