Funnelweb
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There are women who are employed as "mermaids", who do entertainment shows underwater with an air supply which they use intermittently and wearing a tail (and usually a garment covering their breasts).
Actual mermaids are physiologically unlikely as described. Human lungs aren't adapted for removing the dissolved oxygen from water, and the amount of dissolved oxygen in water wouldn't support a mammalian brain which is much bigger than a fish brain. It might be possible that a human appearing mammal could live near the water's surface and breathe air (like whales and dolphins do) and be adapted for prolonged breath-holding.
Mermaids would also need more heat insulation which would require a thick layer of blubber (again like whales and dolphins) unless they lived only in very warm tropical waters. So they wouldn't be the slim sexy maidens we like to picture,
Also the fish reproductive system isn't nearly as fun as the mammalian reproductive system. Mermaids are portrayed with tails resembling scaled fish, which mostly squirt eggs into the water when a male is nearby to squirt sperm into the water. Only a few species of fish bear live young. Fish do not have penises.
JON
It's a nice thought but no I don't
Anonymous
Yes...they come from another planet
Anonymous
Reproduction would be difficult, if their body form is as illustrated!
Obi Wan Knievel
Well, no. I love mermaid lore, but I don't think they actually exist. And since you asked why not, it's because I'm much older than nine.