Magical female figures first appear in cave paintings in the late Paleolithic (Stone Age) period some 30,000 years ago, when modern humans gained dominion over the land and, presumably, began to sail the seas.
According to the NOAA, the post (which eventually went viral on Facebook) was prompted by a recently-aired Animal Planet television special called "Mermaids: The Body Found," that purported to show evidence of the existence of mermaids. The program which aired during "Monster Week" had apparently left some folks a little confused about whether or not mermaids exist after watching it.
If there's one thing worth noting is that the NOAA saying "no evidence of mermaids has been found" which is significantly different to "no evidence of mermaids exists." In the meantime, you can still enjoy watching re-runs of the little mermaid without feeling too sad.