I do not believe mermaids exist because of the biological incompatibility of the two systems. There would firstly be duplication of organs from the human-fish combination. Secondly, the skeletal structures would clash and create more incompatibilities. Thirdly, the structure of a lung would not work. Gills would not be able to work with the body structures of a mermaid.
Also, a mermaid would need to have fragments of fish DNA. DNA has very strong barriers across species. It is difficult for anything larger than a bacteria to take in any DNA from another species. The fish DNA and making it apply to only the legs would be impractical. If a human was to evolve to live in water, it would not evolve into a mermaid.
