I recently published an article on this (which serves as a chapter on a book I am developing on Cornish folklore). Here is the source: Ronald M. James, “Curses, Vengeance, and Fishtails: The Cornish Mermaid in Perspective,” Garry Tregidga (ed.) Cornish Studies: Third Series, Volume One (Exeter, UK: University of Exeter, 2015). Your question can be taken to be addressing either the idea of mermaids or the common legend about mermaids.

The idea of half human half marine animal humans is ubiquitous. This is not surprising because all sorts of cultures imagined half-human half-animal supernatural beings. These traditions are not necessarily linked historically (or prehistorically). Indeed, they are probably not linked. They are more likely expressions of a common, shared human tendency to see the world in these terms. Here is an excerpt from my article addressing the idea of the mermaid:

The belief in sea-dwelling supernatural beings is ancient, and over the years, a number of scholars have examined the history of the motif. In 1880, Llewellynn Jewitt took a position that far-flung examples of half-fish, half-human creatures were linked in some way, and this idea was repeated, to a certain extent, by Arthur Waugh in 1960. Although fish-human deities appear in sources from ancient Mesopotamia, the more removed the examples are from nineteenth-century Northern Europe, the less convincing the connection.

The archetypal mermaid, with fishtail, beautiful form and face, and lavish golden hair, is at the core of the Northern European tradition, and this is precisely what one finds in nineteenth-century Cornish belief. Given the strength of the mermaid tradition in Cornwall, it is not unreasonable to see it as an important source for the image of the sea-going supernatural being in the English-speaking world. That is not to dismiss other inspirations: Hans Christian Andersen’s 1837 Danish literary story, “The Little Mermaid” – and especially its 1989 film incarnation courtesy of Disney – is arguably the most well-known contemporary expression of this type of supernatural being. Even though Andersen’s artistic invention adapted folklore in a distant way, his work has seeped back into popular culture.

Then there is the question about the mermaid legend. That may not be what you're after despite the fact that your question asks about the "mermaid myth." The common Northern European legend involves the abduction of a mermaid from the sea, forcing her to live as a human for a period of time until she can regain access to her original form and return to the ocean. This is widespread in coastal regions of Northern Europe. Like many of these stories, which are usually referred to as Migratory Legends," it is less possible to explain their origin than it is to discuss their distribution and apparent regional changes in the recent past.