Mollies are lovely fish, but sadly misunderstood.
Look, fishes don't misbehave. They aren't like dogs, and there aren't specimens that are well trained and ones that are badly trained. Some are genetically screwed up (all-black angelfish are famously psychotic) but by and large tropical fish do what comes naturally.
Sailfin mollies grow to be 10 to 15 cm long in the wild and live in large groups. The males are constantly looking for females to mate with. They have to, because they are smaller and more likely to be eaten by predators. Moreover, the large sailfin wastes increases drag making them slower than the female mollies. So they need to mate as often as they can because they will die young. What you call nippiness is simply the male molly trying to assert its dominance within the group, in an attempt to monopolise access to the females.
In an aquarium, the male molly doesn't know it's going to live and long and easy life for many years. If you put one male and one female together in a small tank, that female is going to be harassed. It isn't the fish that is being bad, but the fishkeeper. Mollies should be kept in groups, at least 2 females per male, and ideally even more females than that. The tank needs to be big, and it needs lots of hiding places for females to hang out away from the male. Realistically, a group of sailfin mollies probably needs to be kept in an aquarium around the 40 US gallon mark. Shortfin mollies can perhaps get by with a little less, being smaller fish, but 20 US gallons is too small.
I love mollies, and consider them the nicest of the four "common" livebearers. Good quality black mollies are awesome fish. If they weren't so common, people would consider them really amazing fish. What else has that rich, velvet black? In the right tank (big, with brackish water and lots of plants) mollies are simply superb fish.
Cheers,
Neale
Now I'm really confused. At my local fish store one person says mollies are nippers . Another says they are not and are good community fish. A third says only the lyre and hifin are nippers. Which is it?