Mermaids are poorly conceived. The top half of these mythological creatures is human, but they choose to live underwater. While this makes sense when you take into account their fishy lower quarters, mermaids do not have gills. They have a human top half, presumably including a working pair of lungs and the capacity to take in oxygen and expel carbon dioxide. At no point is there the capacity to breathe underwater. Animals which don't need air generally have gills instead, a system which allows them to filter through water for molecules they can process and keep them breathing. Mermaids, on the other half, hang out on rocks and then go home to their underwater lairs. It has never been explained how they can do this without drowning.
If we accept that mermaids can live underwater, let's look at their choice of homeland. They live in giant castles on the sea bed. While the principle of anchoring your home to the ground is academically proven to be the best way to make sure your home doesn't fall off something, that only applies to homes above sea-level. On 'land', there is a force called gravity which pushes downwards. The ground is constantly being kept in place by this force, so therefore a house built on the ground will not wobble around. There are no such guarantees for houses underwater. The sea bed is made of sand, and the weakened gravity that comes from not being above land means there is nothing to hold your house in place. Have you, dear reader, heard of the phenomenon known as "waves"? It basically refers to how water moves around because of the gravitational pull of things like the Moon on our planet. This water movement would knock down any floating house you can build. Despite your house being built on what initially appeared to be solid ground, things would soon prove dangerous as the tides not only push your house but also make the sea bed ripple and buckle.
So we have established that mermaids cannot breathe underwater, nor build lasting homes there. What else do mermaids need to do in order to exist? Oh yes, EAT THINGS. The proportions of a mermaid make them half human and half fish, so they can eat as much food as a person can and excrete as much food as a fish can. Which is to say, eat a lot of food and then get rid of barely any of it. So any mermaids who are not drowning or being crushed in their own houses are imploding due to an improper digestive system. This would obviously look gross, because they'd explode and then their bits would float about in the same place, until some sharks came past and ate them.
Mermaids would need to be fast. The underwater has reduced gravity - this has already been established. How would they hunt unless they used nets? Trident-throwing is impossible underwater. Have you ever attempted it? They don't move anywhere. So mermaids would have to do all their hunting by chasing fish into nets, liek sheepdogs herding sheep into a pen. Their diets would also contain a heightened level of omega 3, which is good for people in doses but lethal in high amounts. So we have mermaids drowning, being crushed, exploding and vomiting up their organs. Which, again, would be gross underwater.
And that's without even considering the threats of sharks, poisoned fish, or ghost-pirates. Mermaids, if they did ever live on our planet, would have died out within a day of existence. And that's why I don't believe in them anymore. They all died.