I took swim lessons at the Y starting age 12 or so (my parents are immigrants and didn't know how to swim themselves, so it took them a while to see the point). After a few years, could manage a mediocre backstroke; enough to keep me alive when doing very slow laps. But I can't float. I sink like a stone.
I was telling this to someone at a party on a hotel rooftop; we were all hanging out in the pool. And she said, "That's ridiculous, everyone can float, I'm a swim instructor, let me teach you." And for half an hour or so, she tried to teach me to float. At the end of which, sounding slightly shocked, she said, "You are the DENSEST person I have ever met."
I felt quite vindicated. But I still can't float.