I can think of three reasons to have a saddle pointing down.
1. You unknowingly raised your saddle too high and need to point it down to effectively lower it. This is the most common reason. You may still be overextending your leg, and since the nose is not supporting your weight on your pubic bone, you might be putting excess weight on the handlebars, causing fatigue to your hands and shoulders.
2. Your handlebar is much lower than your saddle. This might be comfortable and efficient for you. It has become fashionable on road bikes lately but mostly for young and energetic riders.
3. You have unusual anatomy. Perhaps your pubic bone is lower that others' in relation to your sit bones. There are some people who have tried all the various methods of fitting their bikes, starting with the standard ways, and they find that this works for them. You might not experience excess load on your hands and shoulders.
Forgive me for grabbing images from bikeforums. The white bike might fit into the second category but if the owner asked me for advice, I would first check their saddle height.
