No mammal that lives in the sea is half-human either. Obviously mermaids won’t conform 100% to every other sea animal. But we do know that mammals can live in the sea, have forearms, have scales, have breasts, etc. No fish comes close to hitting all the marks that make up a mermaid but mammals hit all of them. The fact that they don’t all come together in a real life creature is just because there aren’t really any mermaids.
Fish all have vertically-oriented asymmetrical tail flukes. Mermaids and aquatic mammals have horizontally-oriented symmetric tail flukes. Aside from the scales (which, as mentioned, some mammals have), mermaid tails are more mammalian than piscine.
Does a mermaid have tits? Yes? Then it’s a mammal.
That depends on the artist. I have seen some paintings which depicted mermaids with vertical flukes. (Can’t find one at the moment. A quick google search turns up a bunch in which the orientation is ambiguous.)
Ah, but they have to be functional (at least potentially). Otherwise, they can just be protuberances, like on a Dalek.
But here’s photographic proof:
Except, of course, for mermaids. 
No mammal that lives in the sea has hands with opposable thumbs either. The possession of hair and breasts pretty much clinches the ID as a mammal, no matter what other attributes the creature might have. There are plenty of other mammals that appear less like a “typical” mammal than a mermaid.
In any case, I have to repeat a meme I saw on Facebook. What if your father was a minotaur, and your mother was a mermaid, but you inherited the human half of each? Then you would just be some guy.
My though was, but you’d have really funky body odor.
This reminds me of Robert De Nero in Meet the Parents: “I have nipples Greg. Can you milk me?”