There is a difference between a mermaid and a siren.
Sirens are born from violent, watery deaths. Drowning, being murdered at sea, their bodies being thrown in to the water shortly after their deaths, stuff like that. They are the ones that sing to sailors (or anyone) and drag them to their deaths when they get too close. They are born anytime.
Mermaids are born when someone who has a great love for the sea (or any other body of water) dies. These deaths have to be peaceful, though people who commit suicide are sometimes brought back at mermaids. All mermaids are born on either solstices or equinoxes.